experiment definition for geometry

Something that can be repeated that has a set of possible results.

Examples: • Rolling dice to see what random numbers come up. • Asking your friends to choose a favorite pet from a list

Experiments help us find out information by collecting data in a careful manner.

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Experiment: Definitions and Examples

Experiment: Definitions, Formulas, & Examples

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Introduction

Experiments are a fundamental part of mathematics, used to test hypotheses and establish relationships between variables. They are used in many fields, including physics, chemistry, biology, psychology, and economics. In this article, we will explore the basics of experiments in math, including definitions, examples, and a quiz to test your understanding.

Definitions

Before we dive into examples, let’s define some key terms related to experiments in math.

• Experiment: A process used to test a hypothesis or investigate a phenomenon. The process involves manipulating one or more variables and measuring the effect on one or more outcomes.
• Hypothesis: A statement or assumption about a phenomenon that is being tested in an experiment.
• Independent variable: The variable that is being manipulated in an experiment. It is also called the predictor variable or the input variable.
• Dependent variable: The variable that is being measured in an experiment. It is also called the response variable or the output variable.
• Control group: A group in an experiment that does not receive the treatment being tested. It is used as a baseline for comparison with the experimental group.
• Experimental group: A group in an experiment that receives the treatment being tested.
• Randomization: The process of randomly assigning subjects to groups in an experiment. This is done to minimize the effect of confounding variables.

Now that we have defined some key terms, let’s explore some examples of experiments in math.

• A scientist wants to test the effect of caffeine on reaction time. She recruits 100 subjects and randomly assigns them to two groups: one group receives caffeine, and the other group receives a placebo. She then measures their reaction time using a computer-based test.
• A researcher wants to test the effect of a new drug on blood pressure. He recruits 200 subjects and randomly assigns them to two groups: one group receives the new drug, and the other group receives a placebo. He then measures their blood pressure at various time points.
• A teacher wants to test the effect of a new teaching method on student performance. She randomly assigns 50 students to two groups: one group receives the new teaching method, and the other group receives the traditional teaching method. She then measures their performance on a standardized test.
• A psychologist wants to test the effect of music on mood. He recruits 30 subjects and randomly assigns them to two groups: one group listens to classical music, and the other group listens to no music. He then measures their mood using a standardized questionnaire.
• An economist wants to test the effect of a tax cut on consumer spending. He collects data on 100 households and measures their spending before and after the tax cut.
• A physicist wants to test the effect of temperature on the viscosity of a liquid. She heats the liquid to different temperatures and measures its viscosity using a viscometer.
• A biologist wants to test the effect of light on plant growth. She grows plants under different light conditions and measures their height and weight after a specified time.
• A mathematician wants to test the effect of an online tutorial on student understanding of a concept. She randomly assigns 50 students to two groups: one group watches the tutorial, and the other group does not. She then measures their understanding using a standardized test.
• A sociologist wants to test the effect of social media on self-esteem. She recruits 100 subjects and randomly assigns them to two groups: one group uses social media for an hour each day, and the other group does not. She then measures their self-esteem using a standardized questionnaire.
• An engineer wants to test the effect of a new manufacturing process on product quality. He randomly assigns 50 products to two groups: one group is manufactured using the new process, and the other group is manufactured using the traditional process. He then measures their quality using a standardized metric.
• What is the purpose of an experiment in math?

The purpose of an experiment in math is to test a hypothesis or investigate a phenomenon by manipulating one or more variables and measuring the effect on one or more outcomes.

• What is the difference between an independent variable and a dependent variable?

The independent variable is the variable that is being manipulated in an experiment, while the dependent variable is the variable that is being measured in the experiment.

• Why is randomization important in experiments?

Randomization is important in experiments because it minimizes the effect of confounding variables and ensures that the groups being compared are as similar as possible, except for the variable being tested.

• What is a control group?

A control group is a group in an experiment that does not receive the treatment being tested. It is used as a baseline for comparison with the experimental group.

• What is a hypothesis?

A hypothesis is a statement or assumption about a phenomenon that is being tested in an experiment.

• What is the purpose of an experiment in math? A) To test a hypothesis or investigate a phenomenon B) To prove a theory C) To collect data randomly D) None of the above
• What is the difference between an independent variable and a dependent variable? A) The independent variable is the variable being measured, and the dependent variable is the variable being manipulated. B) The independent variable is the variable being manipulated, and the dependent variable is the variable being measured. C) There is no difference between the two. D) Both variables are manipulated.
• Why is randomization important in experiments? A) It ensures that the groups being compared are as similar as possible, except for the variable being tested. B) It ensures that the groups being compared are different in every possible way. C) It has no effect on the outcome of the experiment. D) Both A and B.
• What is a control group? A) A group in an experiment that receives the treatment being tested. B) A group in an experiment that does not receive the treatment being tested. C) A group in an experiment that is randomly assigned to a treatment or no-treatment condition. D) Both A and C.
• What is a hypothesis? A) A statement or assumption about a phenomenon that is being tested in an experiment. B) A group in an experiment that receives the treatment being tested. C) A variable being manipulated in an experiment. D) A variable being measured in an experiment.
• A scientist wants to test the effect of exercise on heart rate. She recruits 50 subjects and randomly assigns them to two groups: one group exercises for 30 minutes, and the other group does not. She then measures their heart rate. What is the independent variable? A) Heart rate B) Group assignment (exercise or no exercise) C) Time D) None of the above
• What is the dependent variable in the experiment described in question 6? A) Heart rate B) Group assignment (exercise or no exercise) C) Time D) None of the above
• What is the purpose of a control group? A) To provide a baseline for comparison with the experimental group. B) To manipulate the independent variable. C) To measure the dependent variable. D) Both B and C.
• A researcher wants to test the effect of a new drug on blood sugar levels. He recruits 100 subjects and randomly assigns them to two groups: one group receives the new drug, and the other group receives a placebo. He then measures their blood sugar levels. What is the experimental group in this experiment?
• A researcher wants to test the effect of a new drug on blood sugar levels. He recruits 100 subjects and randomly assigns them to two groups: one group receives the new drug, and the other group receives a placebo. He then measures their blood sugar levels. What is the experimental group in this experiment? A) The group that receives the new drug B) The group that receives the placebo C) Both groups D) Neither group

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Experimental Probability

Experimental probability: introduction, experimental probability: definition, experimental probability formula, solved examples, practice problems, frequently asked questions.

In mathematics, probability refers to the chance of occurrence of a specific event. Probability can be measured on a scale from 0 to 1. The probability is 0 for an impossible event. The probability is 1 if the occurrence of the event is certain.

There are two approaches to study probability: experimental and theoretical. 

Suppose you and your friend toss a coin to decide who gets the first turn to ride a new bicycle. You choose “heads” and your friend chooses “tails.” 

Can you guess who will win? No! You have $\frac{1}{2}$ a chance of winning and so does your friend. This is theoretical since you are predicting the outcome based on what is expected to happen and not on the basis of outcomes of an experiment.

So, what is the experimental probability? Experimental probability is calculated by repeating an experiment and observing the outcomes. Let’s understand this a little better.

Experimental probability, or empirical probability, is the probability calculated by performing actual experiments and gathering or recording the necessary information. How would you define an experiment? The math definition of an experiment is “a process or procedure that can be repeated and that has a set of well-defined possible results or outcomes.”

Consider the same example. Suppose you flip the coin 50 times to see whether you get heads or tails, and you record the outcomes. Suppose you get heads 20 times and tails 30 times. Then the probability calculated using these outcomes is experimental probability. Here, t he experimental meaning is connected with such experiments used to determine the probability of an event.

Now that you know the meaning of experimental probability, let’s understand its formula.

Experimental Probability for an Event A can be calculated as follows:

P(E) $= \frac{Number of occurance of the event A}{Total number of trials}$

Let’s understand this with the help of the last example. 

A coin is flipped a total of 50 times. Heads appeared 20 times. Now, what is the experimental probability of getting heads?

E xperimental probability of getting heads $= \frac{Number of occurrences}{Total number of trials}$

P (Heads) $= \frac{20}{50} = \frac{2}{5}$

P (Tails) $= \frac{30}{50} = \frac{3}{5}$

Experimental Probability vs. Theoretical Probability

Theoretical probability expresses what is expected. On the other hand, experimental probability explains how frequently an event occurred in an experiment.

If you roll a die, the theoretical probability of getting any particular number, say 3, is $\frac{1}{6}$. 

However, if you roll the die 100 times and record how many times 3 appears on top, say 65 times, then the experimental probability of getting 3 is $\frac{65}{100}$.

Theoretical probability for Event A can be calculated as follows:

P(A) $= \frac{Number of outcomes favorable to Event A}{Number of possible outcomes}$

In the example of flipping a coin, the theoretical probability of the occurrence of heads (or tails) on tossing a coin is

P(H) $= \frac{1}{2}$ and  P(T) $= \frac{1}{2}$ (since possible outcomes are $2 -$ head or tail)

Experimental Probability: Examples

Let’s take a look at some of the examples of experimental probability .

Example 1: Ben tried to toss a ping-pong ball in a cup using 10 trials, out of which he succeeded 4 times. 

P(win) $= \frac{Number of success}{Number of trials}$

             $= \frac{4}{10}$

             $= \frac{2}{5}$

Example 2: Two students are playing a game of die. They want to know how many times they land on 2 on the dice if the die is rolled 20 times in a row. 

The experimental probability of rolling a 2 

$= \frac{Number of times 2 appeared}{Number of trials}$

$= \frac{5}{20}$

$= \frac{1}{4}$

1. Probability of an event always lies between 0 and 1.

2. You can also express the probability as a decimal and a percentage.

Experimental probability is a probability that is determined by the results of a series of experiments. Learn more such interesting concepts at SplashLearn .

1. Leo tosses a coin 25 times and observes that the “head” appears 10 times. What is the experimental probability of getting a head?

 P(Head) $= \frac{Number of times heads appeared}{Total number of trials}$

               $= \frac{10}{25}$

               $= \frac{2}{5}$

               $= 0.4$

2. The number of cakes a baker makes per day in a week is given as 7, 8, 6, 10, 2, 8, 3. What is the probability that the baker makes less than 6 cakes the next day?

Solution: 

Number of cakes baked each day in a week $= 7, 8, 6, 10, 2, 8, 3$

Out of 7 days, there were 2 days (highlighted in bold) on which the baker made less than 6 cookies.

P$(< 6 $cookies$) = \frac{2}{7}$

3. The chart below shows the number of times a number was shown on the face of a tossed die. What was the probability of getting a 3 in this experiment?

Number of times 3 showed $= 7$

Number of tosses $= 30$

P(3) $= \frac{7}{30}$

4. John kicked a ball 20 times. He kicked 16 field goals and missed 4 times . What is the experimental probability that John will kick a field goal during the game?

Solution:  

John succeeded in kicking 16 field goals. He attempted to kick a field goal 20 times. 

So, the number of trials $= 20$

John’s experimental probability of kicking a field goal $= \frac{Successful outcomes} {Trials attempted} = \frac{16}{20}$ 

$= \frac{4}{5}$

$= 0.8$ or $80%$

5. James recorded the color of bikes crossing his street. Of the 500 bikes, 10 were custom colors, 100 were white, 50 were red, 120 were black, 100 were silver, 60 were blue, and 60 were gray. What is the probability that the car crossing his street is white?

Number of white bikes $= 100$ 

Total number of bikes $= 500$

P(white bike) $=  \frac{100}{500} = \frac{1}{5}$

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In a class, a student is chosen randomly in five trials to participate in 5 different events. Out of chosen students, 3 were girls and 2 were boys. What is the experimental probability of choosing a boy in the next event?

A manufacturer makes 1000 tablets every month. after inspecting 100 tablets, the manufacturer found that 30 tablets were defective. what is the probability that you will buy a defective tablet, the 3 coins are tossed 1000 times simultaneously and we get three tails $= 160$, two tails $= 260$, one tail $= 320$, no tails $= 260$. what is the probability of occurrence of two tails, the table below shows the colors of shirts sold in a clothing store on a particular day and their respective frequencies. use the table to answer the questions that follow. what is the probability of selling a blue shirt.

Jason leaves for work at the same time each day. Over a period of 327 working days, on his way to work, he had to wait for a train at the railway crossing for 68 days. What is the experimental probability that Jason has to wait for a train on his way to work?

What is the importance of experimental probability?

Experimental probability is widely used in research and experiments in various fields, such as medicine, social sciences, investing, and weather forecasting.

Is experimental probability always accurate?

Predictions based on experimental probability are less reliable than those based on theoretical probability.

Can experimental probability change every time the experiment is performed?

Since the experimental probability is based on the actual results of an experiment, it can change when the results of an experiment change.

What is theoretical probability?

The theoretical probability is calculated by finding the ratio of the number of favorable outcomes to the total number of probable outcomes.

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Definition of Experiment

An experiment is a way of collecting data.

For example, if you want to find out how likely it is for a spinner to land on "yellow", a useful experiment would be to spin the spinner one hundred times, note down which colour it lands on each time, and calculate the fraction of these that are yellow.

Another experiment might involve asking your friends to tell you their favourite computer game and writing down the results.

Description

The aim of this dictionary is to provide definitions to common mathematical terms. Students learn a new math skill every week at school, sometimes just before they start a new skill, if they want to look at what a specific term means, this is where this dictionary will become handy and a go-to guide for a student.

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Learn common math terms starting with letter E

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Basics of an Experiment 

Controlled variables, independent variable, dependent variable, types of experiments, experiment|definition & meaning.

An experiment is a series of procedures and results that are carried out to answer a specific issue or problem or to confirm or disprove a theory or body of knowledge about a phenomenon.

Figure 1: Illustration of an Experiment

The scientific method, a methodical approach to learning about the world around you, is founded on the concept of the experiment . Even while some experiments are conducted in labs, you can conduct an experiment at every time and everywhere.

• The key stages of the scientific process are as follows:
• Keenly Observe things.
• Develop a hypothesis .
• Create and carry out an experiment to verify Your hypothesis.
• Analyze the findings of your experiment.
• Based on the analysis of your results, approve or refute your hypothesis.
• Create a new hypothesis , if required, and evaluate it.

Types of Variables in an Experiment

A variable is, to put it simply, everything that can be altered or managed throughout an experiment. Humidity, the length of the study, the structure of an element, the intensity of sunlight, etc. are typical examples of variables. In any study, there are 3 major types of variables :

• Controlled variables (c.v)
• Independent variables (i.v)
• Dependent variables (d.v).

Figure 2: Illustration of Types of Variables

Variables that are maintained constant or unchangeable are known as controlled variables, sometimes known as constant variables. For instance, if you were evaluating the amount of fizz emitted by various sodas, you may regulate the bottle size to ensure that all soda manufacturers were in 12- ounce bottles. If you were conducting an experiment on the effects of spraying plants with various chemicals, you will attempt to keep a similar pressure and perhaps a similar amount when spraying the plants.

The only variable that  you can modify  is the independent variable. It is one factor as you typically try to adjust one element at a time in experiments. As a result, measuring and interpretation of data are made quite simple. For instance, if you’re attempting to establish whether raising the temperature makes it possible to solvate more amount of sugar in the water, the water temperature is the independent variable. This is the factor that you are consciously in control of.

The variable that is  monitored  to determine whether or not your independent variable has an impact is known as the dependent variable. For instance, in the case where you raise the water temperature to observe if it has an impact on the solubility of sugar in it, the weight or volume of sugar (depending on which one you want to calculate) will be the dependent variable.

There are three main types of experiments. Each has its own pros and cons and is carried out according to the nature of the given scenario and desired outcomes. Following are the names of these three types.

Quasi Experiment

Controlled experiment, field experiment.

Figure 3: Illustration of Types of Experiments

Each of these experiments is discussed below along with their strengths and weaknesses.

These are often conducted in a natural environment and involve measuring the impact of one object on another to determine its impact (D.V.). In Quasi-experiments, the research is simply assessing the impact of an event that is already occurring because there is no intentional modification of the variable in this instance; rather, it is changing naturally.

Owing to the unavailability of the researcher, variables occur   naturally , allowing for easy generalization of results to other (real-life) situations, which leads to greater ecological validity.

Absence of control – Quasi-experiments possess poor internal validity since the experimenter cannot always precisely analyze the impact of the independent variable because there is no influence over the environment or other supplementary variables.

Non-repeatable – Because the researcher has no control over the research process, the validity of the findings cannot be verified.

Controlled experiments are also known as lab experiments . Controlled experiments are carried out under carefully monitored conditions, with the researcher purposefully altering one variable (Independent Variable) to determine how it affects another (dependent Variable).

Control – lab studies have a higher level of environmental and other extrinsic variable control, which allows the scientist to precisely examine the impact of the Independent Variable, increasing internal validity.

Replicable – because of the researcher’s greater degree of control, research techniques may be replicated so that the accuracy of the findings can be verified.

Absence of ecological validity — results are difficult to generalize to other (real-life) situations because of the researcher’s participation in modifying and regulating variables, which leads to poor external validity.

A field experiment could be a controlled or a Quasi-experiment. Instead of taking place in a laboratory, it occurs in the actual world. An illustration of a field experiment could be one that involved an organism in its natural environment.

Validity : Because field experiments are carried out in a natural setting and with a certain level of control, they are considered to possess adequate internal and external validity.

Internal validity is believed to be poorer because there is less control than in lab trials, making it more probable that uncontrollable factors would skew results.

An Example of Identifying the Variables in an Experiment

A farmer wants to determine the effect of different amounts of fertilizer on his crop yield. The farmer does not change the amount of water given to the crop for different amounts of fertilizer applied to the field. Determine which of the variables is the controlled variable, independent variable, and independent variable. Also, mention the reasons behind it.

Figure 4: Illustration of the Example

Controlled variable : The amount of water given to the crop is a controlled variable since it is not changed when different amounts of fertilizer are applied.

Independent variable : The amount of fertilizer added to crops is the independent variable. This is because it is the variable which is being manipulated to determine its impact on crop yield.

Dependent variable : Crop yield is the dependent variable in this example. This is because it is the variable on which the impact of the independent variable (Amount of fertilizer) is being monitored .

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Event Definition < Glossary Index > Exponent Definition

In probability and statistics, an experiment typically refers to a study in which the experimenter is trying to determine whether there is a relationship between two or more variables. In an experiment, the subjects are randomly assigned to either a treatment group or a control group (there can be more than one of either group).

Generally, the control group in an experiment receives a placebo (substance that has no effect) or no treatment at all. The treatment group receives the experimental treatment. The goal of the experiment is to determine whether or not the treatment has the desired/any effect that differs from the control group to a degree that the difference can be attributed to the treatment rather than to random chance or variability. Well-designed experiments can yield informative and unambiguous conclusions about cause and effect relationships.

As an example, if a scientist wants to test whether a new medication they developed has any effect, they would select subjects from a common population and randomly assign them to either a treatment group or a control group. They would then administer the treatment to the treatment group, and either a placebo or no treatment to the control group, and study the effects of each using statistical measures to determine whether the medication had any effect beyond chance or variability.

Note that an experiment does not necessarily need to have a physical treatment. The term "treatment" is used fairly loosely. Another experiment could look at the effects of getting advice from a college counselor on admission rates compared to not getting advice from a college counselor. In this case, the "treatment" would be getting advice from a college counselor. The control group would get no advice from a college counselor.

Importance of experimental design

Like survey methodology , experimental design is essential to the validity of the results of the experiment. A poorly designed experiment can result in false or incorrect conclusions. Proper statistical experiment design generally involves the following:

• Identification of the explanatory variable, also referred to as the independent variable . The explanatory variable is the "treatment," or the thing that causes the change, and can be anything that causes a change in the response variable.
• Identification of the response variable, also referred to as the dependent variable . It is the variable that may be affected by the explanatory/independent variable.
• Defining the population of interest and taking a random sample from the population. Generally the larger the random sample, the less potential for sample error, since the larger sample will likely be more representative of the population.
• Random assignment of the subjects in the sample to either the treatment group or the control group.
• Administration of the treatment to the treatment group, and placebo (or nothing) to the control group), possibly using a blind experiment (the subject doesn't know whether they are receiving the treatment or the placebo) or double blind experiment (neither experimenter nor subject knows which treatment they are getting).
• Measurement of the response over a chosen period of time.
• Statistical analysis of the supposed response to determine whether there is an actual response, or the response can be attributed to chance, to determine whether there is a causal relationship between the treatment and the response.
• Replication of the experiment by peers, assuming there is a causal relationship between the treatment and the response.

Experiments vs surveys

Experiments and surveys are both techniques used as part of inferential statistics . A survey involves the use of a random sample of the population, rather than the whole, with the goal that all subjects in the population have an equal chance of being selected. The random sample of the population is then used to draw conclusions or make inferences about the population as a whole.

In contrast, an experiment typically involves the use of random assignment such that all subjects have an equal chance of being assigned to the groups (treatment and control) in the study, which minimizes potential biases, as well as allows the experimenters to evaluate the role of variability in the experiment. This in turn allows them to determine whether any observed differences between the groups merit further study or not based on whether or not the differences can be attributed to variability or chance.

Experimental Probability

The chance or occurrence of a particular event is termed its probability. The value of a probability lies between 0 and 1 which means if it is an impossible event, the probability is 0 and if it is a certain event, the probability is 1. The probability that is determined on the basis of the results of an experiment is known as experimental probability. This is also known as empirical probability.

What is Experimental Probability?

Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. In mathematical terms, the probability of an event is equal to the number of times an event occurred ÷ the total number of trials. For instance, you flip a coin 30 times and record whether you get a head or a tail. The experimental probability of obtaining a head is calculated as a fraction of the number of recorded heads and the total number of tosses. P(head) = Number of heads recorded ÷ 30 tosses.

Experimental Probability Formula

The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P(E) = Number of times an event occurs/Total number of times the experiment is conducted

Consider an experiment of rotating a spinner 50 times. The table given below shows the results of the experiment conducted. Let us find the experimental probability of spinning the color - blue.

The experimental probability of spinning the color blue = 10/50 = 1/5 = 0.2 = 20%

Experimental Probability vs Theoretical Probability

Experimental results are unpredictable and may not necessarily match the theoretical results. The results of experimental probability are close to theoretical only if the number of trials is more in number. Let us see the difference between experimental probability and theoretical probability.

Experimental Probability Examples

Here are a few examples from real-life scenarios.

a) The number of cookies made by Patrick per day in this week is given as 4, 7, 6, 9, 5, 9, 5.

Based on this data, what is the reasonable estimate of the probability that Patrick makes less than 6 cookies the next day?

P(< 6 cookies) = 3/7 = 0.428 = 42%

b) Find the reasonable estimate of the probability that while ordering a pizza, the next order will not be of a pepperoni topping.

Based on this data , the reasonable estimate of the probability that the next type of toppings that would get ordered is not a pepperoni will be 15/20 = 3/4 = 75%

Related Sections

• Card Probability
• Conditional Probability Calculator
• Binomial Probability Calculator
• Probability Rules
• Probability and Statistics

Important Notes

• The sum of the experimental probabilities of all the outcomes is 1.
• The probability of an event lies between 0 and 1, where 0 is an impossible event and 1 denotes a certain event.
• Probability can also be expressed in percentage.

Examples on Experimental Probability

Example 1: The following table shows the recording of the outcomes on throwing a 6-sided die 100 times.

Find the experimental probability of: a) Rolling a four; b) Rolling a number less than four; c) Rolling a 2 or 5

Experimental probability is calculated by the formula: Number of times an event occurs/Total number of trials

a) Rolling a 4: 17/100 = 0.17

b) Rolling a number less than 4: 56/100 = 0.56

c) Rolling a 2 or 5: 31/100 = 0.31

Example 2: The following set of data shows the number of messages that Mike received recently from 6 of his friends. 4, 3, 2, 1, 6, 8. Based on this, find the probability that Mike will receive less than 2 messages next time.

Mike has received less than 2 messages from 2 of his friends out of 6.

Therefore, P(<2) = 2/6 = 1/3

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Practice Questions on Experimental Probability

Frequently asked questions (faqs), how do you find the experimental probability.

The experimental probability of an event is based on actual experiments and the recordings of the events. It is equal to the number of times an event occurred divided by the total number of trials.

What is the Experimental Probability of rolling a 6?

The experimental probability of rolling a 6 is 1/6. A die has 6 faces numbered from 1 to 6. Rolling the die to get any number from 1 to 6 is the same and the probability (of getting a 6) = Number of favorable outcomes/ total possible outcomes = 1/6.

What is the Difference Between Theoretical and Experimental Probability?

Theoretical probability is what is expected to happen and experimental probability is what has actually happened in the experiment.

Do You Simplify Experimental Probability?

Yes, after finding the ratio of the number of times the event occurred to the total number of trials conducted, the fraction which is obtained is simplified.

Which Probability is More Accurate, Theoretical Probability or Experimental Probability?

Theoretical probability is more accurate than experimental probability. The results of experimental probability are close to theoretical only if the number of trials are more in number.

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Theoretical and experimental probabilities.

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Difference between axioms, theorems, postulates, corollaries, and hypotheses

I've heard all these terms thrown about in proofs and in geometry, but what are the differences and relationships between them? Examples would be awesome! :)

• terminology

• 3 $\begingroup$ Go read this Wikipedia article and the articles it links to. $\endgroup$ –  kahen Commented Oct 24, 2010 at 20:22
• 10 $\begingroup$ One difficulty is that, for historical reasons, various results have a specific term attached (Parallel postulate, Zorn's lemma, Riemann hypothesis, Collatz conjecture, Axiom of determinacy). These do not always agree with the the usual usage of the words. Also, some theorems have unique names, for example Hilbert's Nullstellensatz. Since the German word there incorporates "satz", which means "theorem", it is not typical to call this the "Nullstellensatz theorem". These things make it harder to pick up the general usage. $\endgroup$ –  Carl Mummert Commented Oct 24, 2010 at 23:15

5 Answers 5

In Geometry, " Axiom " and " Postulate " are essentially interchangeable. In antiquity, they referred to propositions that were "obviously true" and only had to be stated, and not proven. In modern mathematics there is no longer an assumption that axioms are "obviously true". Axioms are merely 'background' assumptions we make. The best analogy I know is that axioms are the "rules of the game". In Euclid's Geometry, the main axioms/postulates are:

• Given any two distinct points, there is a line that contains them.
• Any line segment can be extended to an infinite line.
• Given a point and a radius, there is a circle with center in that point and that radius.
• All right angles are equal to one another.
• If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. (The parallel postulate ).

A theorem is a logical consequence of the axioms. In Geometry, the "propositions" are all theorems: they are derived using the axioms and the valid rules. A "Corollary" is a theorem that is usually considered an "easy consequence" of another theorem. What is or is not a corollary is entirely subjective. Sometimes what an author thinks is a 'corollary' is deemed more important than the corresponding theorem. (The same goes for " Lemma "s, which are theorems that are considered auxiliary to proving some other, more important in the view of the author, theorem).

A " hypothesis " is an assumption made. For example, "If $x$ is an even integer, then $x^2$ is an even integer" I am not asserting that $x^2$ is even or odd; I am asserting that if something happens (namely, if $x$ happens to be an even integer) then something else will also happen. Here, "$x$ is an even integer" is the hypothesis being made to prove it.

See the Wikipedia pages on axiom , theorem , and corollary . The first two have many examples.

• 2 $\begingroup$ Arturo, I hope you don't mind if I edged your already excellent answer a little bit nearer to perfection. $\endgroup$ –  J. M. ain't a mathematician Commented Oct 25, 2010 at 0:26
• $\begingroup$ @J.M.: Heh. Not at all; thanks for the corrections! You did miss the single quotation mark after "propositions" in the second paragraph, though. (-: $\endgroup$ –  Arturo Magidin Commented Oct 25, 2010 at 0:33
• $\begingroup$ Great answer. Clear and informal, while still accurate. Better than wikipedia's, in my opinion. $\endgroup$ –  7hi4g0 Commented Feb 8, 2014 at 0:47
• $\begingroup$ Why is Bertrand's postulate considered a postulate? I don't think it would be obvious to anybody except to extraordinary geniuses like Euler, Gauss or Ramanujan.. $\endgroup$ –  AvZ Commented Feb 14, 2015 at 5:54
• 1 $\begingroup$ @gen-zreadytoperish: People don’t use usually use “postulate” anymore outside of historical contexts (e.g., “Bertrand’s postulate”). $\endgroup$ –  Arturo Magidin Commented Apr 12, 2020 at 20:26

Based on logic, an axiom or postulate is a statement that is considered to be self-evident. Both axioms and postulates are assumed to be true without any proof or demonstration. Basically, something that is obvious or declared to be true and accepted but have no proof for that, is called an axiom or a postulate. Axioms and postulate serve as a basis for deducing other truths.

The ancient Greeks recognized the difference between these two concepts. Axioms are self-evident assumptions, which are common to all branches of science, while postulates are related to the particular science.

Aristotle by himself used the term “axiom”, which comes from the Greek “axioma”, which means “to deem worth”, but also “to require”. Aristotle had some other names for axioms. He used to call them as “the common things” or “common opinions”. In Mathematics, Axioms can be categorized as “Logical axioms” and “Non-logical axioms”. Logical axioms are propositions or statements, which are considered as universally true. Non-logical axioms sometimes called postulates, define properties for the domain of specific mathematical theory, or logical statements, which are used in deduction to build mathematical theories. “Things which are equal to the same thing, are equal to one another” is an example for a well-known axiom laid down by Euclid.

The term “postulate” is from the Latin “postular”, a verb which means “to demand”. The master demanded his pupils that they argue to certain statements upon which he could build. Unlike axioms, postulates aim to capture what is special about a particular structure. “It is possible to draw a straight line from any point to any other point”, “It is possible to produce a finite straight continuously in a straight line”, and “It is possible to describe a circle with any center and any radius” are few examples for postulates illustrated by Euclid.

What is the difference between Axioms and Postulates?

• An axiom generally is true for any field in science, while a postulate can be specific on a particular field.

• It is impossible to prove from other axioms, while postulates are provable to axioms.

• $\begingroup$ Hmmm. This isn't a bad explanation, and thanks for attempting to explain the difference, but I'm still a bit fuzzy on the historical distinction as used by Aristotle and Euclid. $\endgroup$ –  Wildcard Commented Dec 10, 2016 at 2:53
• $\begingroup$ The historical part is interesting but at the end your statements are not correct. It is not the way the words "axiom" and "postulate" are being used in math and logic. $\endgroup$ –  LoMaPh Commented Jun 18, 2017 at 9:16

Technically Axioms are self-evident or self-proving, while postulates are simply taken as given. However really only Euclid and really high end theorists and some poly-maths make such a distinction. See http://www.friesian.com/space.htm

Theorems are then derived from the "first principles" i.e. the axioms and postulates.

• 3 $\begingroup$ No, that "technical" division really leads nowhere, and nowadays no one follows it. $\endgroup$ –  Andrés E. Caicedo Commented Nov 23, 2014 at 17:58
• 2 $\begingroup$ From a purely epistemological standpoint this is an excellent distinction, and I am extremely glad you took the time to contribute this simple answer. This fully clarified the historical difference for me. While @AndrésE.Caicedo is correct that this distinction doesn't form a part of modern mathematical practice, that doesn't make it wholly valueless. $\endgroup$ –  Wildcard Commented Dec 10, 2016 at 3:03

Axiom: Not proven and known to be unprovable using other axioms

Postulate: Not proven but not known if it can be proven from axioms (and theorems derived only from axioms)

Theorem: Proved using axioms and postulates

For example -- the parallel postulate of Euclid was used unproven but for many millennia a proof was thought to exist for it in terms of other axioms. Later is was definitively shown that it could not (by e.g. showing consistent other geometries). At that point it could be converted to axiom status for the Euclidean geometric system.

I think everything being marked as postulates is a bit of a disservice, but also reflect it would be almost impossible to track if any nontrivial theorem does not somewhere depend on a postulate rather than an axiom, also, standards for what constitutes 'proof' changes over time.

But I do think the triple structure is helpful for teaching beginning students. E.g. you can prove congruence of triangles via SSS with some axioms but it can be damnably hard and confusing/circular/nit-picky, so it makes sense to teach it as a postulate at first, use it, and then come back and show a proof.

• $\begingroup$ I think that the common usage does not require that an axiom is "known to be unprovable using other axioms." This would mean that there is no such thing as "an axiom", only "an axiom relative to other statements"; and it would mean that many common presentations of axioms actually don't consist of axioms. (For example, the axioms of a ring include left and right distributivity of multiplication over addition; the axioms of a commutative ring include commutativity of multiplication; but suddenly that means that we must (arbitrarily) pick only left or right distributivity as an axiom.) $\endgroup$ –  LSpice Commented Mar 6, 2018 at 14:39

Since it is not possible to define everything, as it leads to a never ending infinite loop of circular definitions, mathematicians get out of this problem by imposing "undefined terms". Words we never define. In most mathematics that two undefined terms are set and element of .

We would like to be able prove various things concerning sets. But how can we do so if we never defined what a set is? So what mathematicians do next is impose a list of axioms . An axiom is some property of your undefined object. So even though you never define your undefined terms you have rules about them. The rules that govern them are the axioms . One does not prove an axiom, in fact one can choose it to be anything he wishes (of course, if it is done mindlessly it will lead to something trivial).

Now that we have our axioms and undefined terms we can form some main definitions for what we want to work with.

After we defined some stuff we can write down some basic proofs. Usually known as propositions . Propositions are those mathematical facts that are generally straightforward to prove and generally follow easily form the definitions.

Deep propositions that are an overview of all your currently collected facts are usually called Theorems . A good litmus test, to know the difference between a Proposition and Theorem, as somebody once remarked here, is that if you are proud of a proof you call it a Theorem, otherwise you call it a Proposition. Think of a theorem as the end goals we would like to get, deep connections that are also very beautiful results.

Sometimes in proving a Proposition or a Theorem we need some technical facts. Those are called Lemmas . Lemmas are usually not useful by themselves. They are only used to prove a Proposition/Theorem, and then we forget about them.

The net collection of definitions, propositions, theorems, form a mathematical theory .

• 1 $\begingroup$ Please don't propound the falsehood that "it is not possible to define everything." I understand what you mean by it, but the result is only pedagogical disaster. (See my answer here.) The truth is that a concept or thought is a distinct entity from a symbolic representation, and when a concept is grasped directly, total understanding is possible in spite of the apparent circularity of defining words using other words. $\endgroup$ –  Wildcard Commented Dec 10, 2016 at 2:58

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What Is an Experiment? Definition and Design

The Basics of an Experiment

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Science is concerned with experiments and experimentation, but do you know what exactly an experiment is? Here's a look at what an experiment is... and isn't!

Key Takeaways: Experiments

• An experiment is a procedure designed to test a hypothesis as part of the scientific method.
• The two key variables in any experiment are the independent and dependent variables. The independent variable is controlled or changed to test its effects on the dependent variable.
• Three key types of experiments are controlled experiments, field experiments, and natural experiments.

What Is an Experiment? The Short Answer

In its simplest form, an experiment is simply the test of a hypothesis . A hypothesis, in turn, is a proposed relationship or explanation of phenomena.

Experiment Basics

The experiment is the foundation of the scientific method , which is a systematic means of exploring the world around you. Although some experiments take place in laboratories, you could perform an experiment anywhere, at any time.

Take a look at the steps of the scientific method:

• Make observations.
• Formulate a hypothesis.
• Design and conduct an experiment to test the hypothesis.
• Evaluate the results of the experiment.
• Accept or reject the hypothesis.
• If necessary, make and test a new hypothesis.

Types of Experiments

• Natural Experiments : A natural experiment also is called a quasi-experiment. A natural experiment involves making a prediction or forming a hypothesis and then gathering data by observing a system. The variables are not controlled in a natural experiment.
• Controlled Experiments : Lab experiments are controlled experiments , although you can perform a controlled experiment outside of a lab setting! In a controlled experiment, you compare an experimental group with a control group. Ideally, these two groups are identical except for one variable , the independent variable .
• Field Experiments : A field experiment may be either a natural experiment or a controlled experiment. It takes place in a real-world setting, rather than under lab conditions. For example, an experiment involving an animal in its natural habitat would be a field experiment.

Variables in an Experiment

Simply put, a variable is anything you can change or control in an experiment. Common examples of variables include temperature, duration of the experiment, composition of a material, amount of light, etc. There are three kinds of variables in an experiment: controlled variables, independent variables and dependent variables .

Controlled variables , sometimes called constant variables are variables that are kept constant or unchanging. For example, if you are doing an experiment measuring the fizz released from different types of soda, you might control the size of the container so that all brands of soda would be in 12-oz cans. If you are performing an experiment on the effect of spraying plants with different chemicals, you would try to maintain the same pressure and maybe the same volume when spraying your plants.

The independent variable is the one factor that you are changing. It is one factor because usually in an experiment you try to change one thing at a time. This makes measurements and interpretation of the data much easier. If you are trying to determine whether heating water allows you to dissolve more sugar in the water then your independent variable is the temperature of the water. This is the variable you are purposely controlling.

The dependent variable is the variable you observe, to see whether it is affected by your independent variable. In the example where you are heating water to see if this affects the amount of sugar you can dissolve , the mass or volume of sugar (whichever you choose to measure) would be your dependent variable.

Examples of Things That Are Not Experiments

• Making a model volcano.
• Making a poster.
• Changing a lot of factors at once, so you can't truly test the effect of the dependent variable.
• Trying something, just to see what happens. On the other hand, making observations or trying something, after making a prediction about what you expect will happen, is a type of experiment.
• Bailey, R.A. (2008). Design of Comparative Experiments . Cambridge: Cambridge University Press. ISBN 9780521683579.
• Beveridge, William I. B., The Art of Scientific Investigation . Heinemann, Melbourne, Australia, 1950.
• di Francia, G. Toraldo (1981). The Investigation of the Physical World . Cambridge University Press. ISBN 0-521-29925-X.
• Hinkelmann, Klaus and Kempthorne, Oscar (2008). Design and Analysis of Experiments, Volume I: Introduction to Experimental Design (Second ed.). Wiley. ISBN 978-0-471-72756-9.
• Shadish, William R.; Cook, Thomas D.; Campbell, Donald T. (2002). Experimental and quasi-experimental designs for generalized causal inference (Nachdr. ed.). Boston: Houghton Mifflin. ISBN 0-395-61556-9.
• Examples of Independent and Dependent Variables
• Difference Between Independent and Dependent Variables
• Null Hypothesis Examples
• Six Steps of the Scientific Method
• How To Design a Science Fair Experiment
• Independent Variable Definition and Examples
• Scientific Method Vocabulary Terms
• Understanding Simple vs Controlled Experiments
• Understanding Experimental Groups
• The Difference Between Control Group and Experimental Group
• Scientific Method Flow Chart
• Dependent Variable Definition and Examples
• Scientific Variable
• What Is a Controlled Experiment?
• What Are the Elements of a Good Hypothesis?

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Experimental Probability – Definition with Examples

Created on Jan 09, 2024

Updated on January 9, 2024

At Brighterly , we believe that a solid understanding of mathematics can empower our children to do great things. That’s why we’re committed to making complex math concepts accessible, engaging, and fun for all children. Among the myriad of mathematical topics we cover, one of the more practical, yet fascinating, is experimental probability.

Experimental probability is like the bridge between math and the real world, offering a hands-on approach to understanding likelihood and chance. It’s all about observation, data collection, and making sense of the patterns that emerge. Experimental probability takes us beyond the theoretical and into the empirical, providing our children with a richer, fuller understanding of how probability works.

What Is Experimental Probability?

Experimental probability is a concept that children often encounter in their mathematical journey, and it provides a fantastic way to understand how probability works in the real world. It is a type of probability that we calculate based on the outcomes of an experiment or activity, as opposed to theoretical probability which we calculate using mathematical principles. It’s all about doing rather than just thinking.

Imagine you’re flipping a coin. The theoretical probability of getting a heads or tails is 50%, or 0.5, because these are the only two possible outcomes. However, if you flip the coin 10 times and get 7 heads and 3 tails, the experimental probability of getting heads is 70% (or 0.7), and for tails, it’s 30% (or 0.3). This is because experimental probability depends on the actual results of the experiment.

Definition of Experimental Probability

The definition of experimental probability is the ratio of the number of times an event occurs to the total number of trials or times the activity is performed. It is calculated after conducting an experiment or activity, and can often differ from theoretical probability because of the variability and unpredictability of real-world events.

Calculating Experimental Probability

The process of calculating experimental probability involves two steps: conducting the experiment to gather data, and then using that data to calculate the probability. The formula for calculating experimental probability is:

P(E) = Number of times event E occurs / Total number of trials

For example, if you roll a dice 60 times, and the number 4 comes up 15 times, the experimental probability of rolling a 4 is calculated as 15 (the number of times 4 occurs) divided by 60 (the total number of trials), which equals 0.25, or 25%.

Examples of Experimental Probability

To better understand this concept, let’s explore some real-world examples of experimental probability:

In a bag of 30 marbles, 10 are blue, 10 are green, and 10 are red. If you randomly pick a marble 30 times, replacing the marble each time, and you get 12 blue, 8 green, and 10 red marbles, the experimental probability for each color would be calculated as follows:

• Blue: 12/30 = 0.4 or 40%
• Green: 8/30 = 0.267 or 26.7%
• Red: 10/30 = 0.333 or 33.3%

In a deck of 52 playing cards, if you draw a card 52 times, replacing the card each time, and you draw a heart 15 times, the experimental probability of drawing a heart is 15/52 = 0.288 or 28.8%.

Properties of Experimental Probability

Experimental probability, as with any type of probability, possesses some key properties. It will always be a value between 0 and 1 (or 0% and 100% when expressed as a percentage). This makes sense, as it’s impossible for an event to occur less than 0 times (probability = 0), or more times than the total number of trials (probability = 1).

Another key property is that the sum of the probabilities of all possible outcomes will equal 1. For example, in our earlier coin flipping example, the sum of the experimental probabilities for getting heads (0.7) and tails (0.3) equals 1.

Key Factors Affecting Experimental Probability

The key factor affecting experimental probability is the number of trials. In general, the more trials are performed, the closer the experimental probability gets to the theoretical probability. This principle is known as the Law of Large Numbers.

Other factors that can affect experimental probability include inaccuracies in data collection and environmental variables, such as the fairness of a coin or die, the method of drawing cards, and so on.

Difference Between Experimental and Theoretical Probability

The main difference between experimental and theoretical probability lies in their calculation methods. Theoretical probability is determined mathematically, using the known outcomes of an event, while experimental probability is determined empirically, using data from actual trials of the event.

In theory, a coin has a 50% chance of landing on heads, but in an experiment, it might not. Over the long run, the experimental probability will likely get closer to the theoretical probability, thanks to the Law of Large Numbers.

Formulas for Calculating Experimental Probability

As mentioned earlier, the formula for calculating experimental probability is straightforward:

Here, ‘P(E)’ represents the probability of event E occurring.

Writing Formulas for Experimental Probability

Let’s get into the details of how to write formulas for experimental probability. For any given event E, you can express the experimental probability of that event occurring as a fraction, decimal, or percentage using the aforementioned formula. Just remember to divide the number of times the event occurred by the total number of trials.

For example, if you’re trying to find the experimental probability of drawing a heart from a deck of cards and you drew a heart 13 times out of 52 trials, you’d write it as follows:

P(Heart) = 13/52 ≈ 0.25 = 25%

Use Cases of Experimental Probability in Real Life

Experimental probability finds its use in various real-life scenarios, from games and sports to weather forecasting and medical research. For example, predicting the outcome of a football game based on past performances is a use of experimental probability. Likewise, weather forecasts use data from previous years to predict the likelihood of certain weather conditions. Experimental probability is also used in clinical trials to determine the effectiveness of a new drug or treatment.

Practice Problems on Experimental Probability

To fully understand experimental probability, it’s helpful to solve some practice problems. Try the following scenarios:

• You toss a coin 50 times and get heads 29 times. What is the experimental probability of getting heads?
• You draw a card from a deck of 52 cards 100 times and draw a queen 22 times. What is the experimental probability of drawing a queen?
• You roll a die 200 times and roll a 5, 40 times. What is the experimental probability of rolling a 5?

In conclusion, experimental probability offers a practical and exciting way for children to understand the concept of probability and chance. Through experiments and observations, children can learn not just how to calculate the likelihood of an event, but also develop an intuitive understanding of probability.

At Brighterly, we encourage our young learners to immerse themselves in the world of experimental probability and explore its numerous applications in real-life situations. From games and sports to weather forecasting and medical research, experimental probability has vast real-world significance. Remember, with more trials, the experimental probability tends to converge with the theoretical probability, making it a valuable tool in understanding uncertainty and making predictions.

Frequently Asked Questions on Experimental Probability

What is the formula for experimental probability.

The formula for experimental probability is: P(E) = Number of times event E occurs / Total number of trials. Here, P(E) stands for the probability of event E, which could be any event you’re examining. This formula is straightforward to use, and it allows you to compute the experimental probability accurately using your collected data.

How is experimental probability calculated?

Experimental probability is calculated by carrying out an experiment and recording the outcomes. The number of times a particular event occurs is then divided by the total number of trials conducted. For example, if you roll a dice 100 times and the number 4 comes up 20 times, the experimental probability of rolling a 4 would be 20/100 = 0.20, or 20%.

What is the difference between experimental and theoretical probability?

Theoretical probability and experimental probability differ in the ways they are determined. Theoretical probability is derived using mathematical principles, considering all possible outcomes of an event. For instance, when flipping a fair coin, the theoretical probability of getting a head is 50% since there are two equally likely outcomes – heads and tails. On the other hand, experimental probability is calculated based on actual experiments or trials. If you flip the same coin 100 times and get heads 60 times, the experimental probability of getting heads would be 60/100 = 0.60, or 60%. Over time, with a large number of trials, the experimental probability will tend to get closer to the theoretical probability. This is a consequence of the Law of Large Numbers.

• Britannica: Law of Large Numbers
• Coursera: Understanding Experimental Probability
• Wolfram MathWorld: Experimental Probability

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It's not as world-famous as ramen or sushi. But the humble onigiri is soul food in Japan

The word “onigiri” (OH-knee-GEEH-reeh) just became part of the Oxford English Dictionary this year

TOKYO — The word “onigiri” became part of the Oxford English Dictionary this year, proof that the humble sticky-rice ball and mainstay of Japanese food has entered the global lexicon.

The rice balls are stuffed with a variety of fillings and typically wrapped in seaweed. It’s an everyday dish that epitomizes “washoku” — the traditional Japanese cuisine that was designated a UNESCO Intangible Cultural Heritage a decade ago.

Onigiri is “fast food, slow food and soul food,” says Yusuke Nakamura, who heads the Onigiri Society, a trade group in Tokyo.

Fast because you can find it even at convenience stores. Slow because it uses ingredients from the sea and mountains, he said. And soul food because it’s often made and consumed among family and friends. No tools are needed, just gently cupped hands.

“It’s also mobile, food on the move,” he said.

Onigiri in its earliest form is believed to go back at least as far as the early 11th Century; it’s mentioned in Murasaki Shikibu’s “The Tale of Genji.” It appears in Akira Kurosawa’s classic 1954 film “Seven Samurai” as the ultimate gift of gratitude from the farmers.

What exactly goes into onigiri?

The sticky characteristic of Japanese rice is key.

What's placed inside is called “gu,” or filling. A perennial favorite is umeboshi, or salted plum. Or perhaps mentaiko, which is hot, spicy roe. But in principle, anything can be placed inside onigiri, even sausages or cheese.

Then the ball is wrapped with seaweed. Even one nice big onigiri would make a meal, although many people would eat more.

Some stand by the classic onigiri

Yosuke Miura runs Onigiri Asakusa Yadoroku, a restaurant founded in 1954 by his grandmother. Yadoroku, which roughly translates to “good-for-nothing,” is named for her husband, Miura’s grandfather. It claims to be the oldest onigiri restaurant in Tokyo.

There are just two tables. The counter has eight chairs. Takeout is an option, but you still have to stand in line.

“Nobody dislikes onigiri,” said Miura, smiling behind a wooden counter. In a display case before him are bowls of gu, including salmon, shrimp and miso-flavored ginger. “It’s nothing special basically. Every Japanese has 100% eaten it.”

Also a classical flautist, Miura sees onigiri as a score handed down from his grandmother, one which he will reproduce faithfully.

“In classical music, you play what’s written on the music sheet. Onigiri is the same,” he says. “You don’t try to do something new.”

Yadoruku is tucked away in the quaint old part of Tokyo called Asakusa. It opens at 11:30 a.m. and closes when it runs out of rice, usually within the hour. Then it opens again for dinner. The most expensive onigiri costs 770 yen ($4.90), with salmon roe, while the cheapest is 319 yen ($2). That includes miso soup. No reservations are taken.

Although onigiri can be round or square, animal or star-shaped, Miura’s standard is the triangular ones. He makes them to order, right before your eyes, taking just 30 seconds for each.

He places the hot rice in triangular molds that look like cookie cutters, rubs salt on his hands and then cups the rice — three times to gently firm the sides. The crisp nori, or seaweed, is wrapped like a kerchief around the rice, with one end up so it stays crunchy.

The first bite is just nori and rice. The gu comes with your second bite.

“The Yadoroku onigiri will not change until the end of Earth,” Miura said with a grin.

Others want to experiment

Miyuki Kawarada runs Taro Tokyo Onigiri, which has four outlets in Japan. She is eyeing Los Angeles, too, and then Paris. Her vision: to make onigiri “the world’s fast food.”

The name Taro was chosen because it’s common, the Japanese equivalent of John or Michael. Onigiri, she says, has mass appeal because it’s simple to make, is gluten-free and is versatile.

And other Japanese foods like ramen and sushi have found worldwide popularity , she notes.

At her cheerful, modern shop, workers wearing khaki-colored company T-shirts busily prepare the gu and rice balls in a kitchen visible behind the cash register. The shop only serves takeout.

Kawarada’s onigiri has lots of gu on top, for colorful toppings, instead of inside. Each one comes with a separately wrapped piece of nori to be placed around it right before you eat.

Her gu gets adventurous. Cream cheese is mixed with a pungent Japanese pickle called “iburigakko,” for instance, and each onigiri costs 250 yen ($1.60). Spam and egg onigiri costs 300 yen ($1.90); the one adorned with several types of “kombu,” or edible kelp, called “Dashi Punch X3,” costs 280 yen ($1.80).

“Onigiri is the infinite universe. We don’t get tied down in tradition,” said Kawarada.

The customers

Asami Hirano, who stopped in while walking her dog, took a long time choosing her meal at Taro Tokyo Onigiri on a recent day.

“I’ve always loved onigiri since I was a kid. My mother made them,” she said.

Nicolas Foo Cheung, a Frenchman who works nearby as an intern, had been to Taro Tokyo Onigiri a few times before and thinks it’s a good deal. “It’s simple food,” he said.

Miki Yamada, a food promoter, intentionally calls onigiri “omusubi,” the other common word for rice balls, because the latter more clearly refers to the idea of connections. She says her life’s mission is to bring people together, especially since the triple earthquake, tsunami and nuclear disasters hit her family’s rice farm in Fukushima, northeastern Japan, in 2011.

“By facing up to omusubi, I have encountered a spirituality, a basic Japanese-ness of sorts,” she said.

There is nothing better, she said, than plain Aizu rice omusubi with a pinch of salt and utterly nothing inside.

“It energizes you. It’s that ultimate comfort food,” she said.

Yuri Kageyama is on X: https://twitter.com/yurikageyama