introduction to probability homework answers

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Unit 7: Probability

About this unit.

Probability tells us how often some event will happen after many repeated trials. You've experienced probability when you've flipped a coin, rolled some dice, or looked at a weather forecast. Go deeper with your understanding of probability as you learn about theoretical, experimental, and compound probability, and investigate permutations, combinations, and more!

Basic theoretical probability

• Intro to theoretical probability (Opens a modal)
• Probability: the basics (Opens a modal)
• Simple probability: yellow marble (Opens a modal)
• Simple probability: non-blue marble (Opens a modal)
• Intuitive sense of probabilities (Opens a modal)
• The Monty Hall problem (Opens a modal)
• Simple probability Get 5 of 7 questions to level up!
• Comparing probabilities Get 5 of 7 questions to level up!

Probability using sample spaces

• Example: All the ways you can flip a coin (Opens a modal)
• Die rolling probability (Opens a modal)
• Subsets of sample spaces (Opens a modal)
• Subsets of sample spaces Get 3 of 4 questions to level up!

Basic set operations

• Intersection and union of sets (Opens a modal)
• Relative complement or difference between sets (Opens a modal)
• Universal set and absolute complement (Opens a modal)
• Subset, strict subset, and superset (Opens a modal)
• Bringing the set operations together (Opens a modal)
• Basic set notation Get 5 of 7 questions to level up!

Experimental probability

• Experimental probability (Opens a modal)
• Theoretical and experimental probabilities (Opens a modal)
• Making predictions with probability (Opens a modal)
• Simulation and randomness: Random digit tables (Opens a modal)
• Experimental probability Get 5 of 7 questions to level up!
• Making predictions with probability Get 5 of 7 questions to level up!

Randomness, probability, and simulation

• Experimental versus theoretical probability simulation (Opens a modal)
• Theoretical and experimental probability: Coin flips and die rolls (Opens a modal)
• Random number list to run experiment (Opens a modal)
• Random numbers for experimental probability (Opens a modal)
• Statistical significance of experiment (Opens a modal)
• Interpret results of simulations Get 3 of 4 questions to level up!

Addition rule

• Probability with Venn diagrams (Opens a modal)
• Addition rule for probability (Opens a modal)
• Addition rule for probability (basic) (Opens a modal)
• Adding probabilities Get 3 of 4 questions to level up!
• Two-way tables, Venn diagrams, and probability Get 3 of 4 questions to level up!

Multiplication rule for independent events

• Sample spaces for compound events (Opens a modal)
• Compound probability of independent events (Opens a modal)
• Probability of a compound event (Opens a modal)
• "At least one" probability with coin flipping (Opens a modal)
• Free-throw probability (Opens a modal)
• Three-pointer vs free-throw probability (Opens a modal)
• Probability without equally likely events (Opens a modal)
• Independent events example: test taking (Opens a modal)
• Die rolling probability with independent events (Opens a modal)
• Probabilities involving "at least one" success (Opens a modal)
• Sample spaces for compound events Get 3 of 4 questions to level up!
• Independent probability Get 3 of 4 questions to level up!
• Probabilities of compound events Get 3 of 4 questions to level up!
• Probability of "at least one" success Get 3 of 4 questions to level up!

Multiplication rule for dependent events

• Dependent probability introduction (Opens a modal)
• Dependent probability: coins (Opens a modal)
• Dependent probability example (Opens a modal)
• Independent & dependent probability (Opens a modal)
• The general multiplication rule (Opens a modal)
• Dependent probability (Opens a modal)
• Dependent probability Get 3 of 4 questions to level up!

Conditional probability and independence

• Calculating conditional probability (Opens a modal)
• Conditional probability explained visually (Opens a modal)
• Conditional probability using two-way tables (Opens a modal)
• Conditional probability tree diagram example (Opens a modal)
• Tree diagrams and conditional probability (Opens a modal)
• Conditional probability and independence (Opens a modal)
• Analyzing event probability for independence (Opens a modal)
• Calculate conditional probability Get 3 of 4 questions to level up!
• Dependent and independent events Get 3 of 4 questions to level up!

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Unit 12 – Probability

Introduction to Probability

LESSON/HOMEWORK

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Sets and Probability

Adding Probabilities

Conditional Probability

Independent Events

Multiplying Probabilities

Unit Review

Unit 12 Review – Probability

UNIT REVIEW

EDITABLE REVIEW

Unit 12 Assessment Form A

EDITABLE ASSESSMENT

Unit 12 Assessment Form B

Unit 12 Assessment Form C

Unit 12 Assessment Form D

Unit 12 Exit Tickets

Unit 12 Mid-Unit Quiz (Through Lesson 4) – Form A

Unit 12 Mid-Unit Quiz (Through Lesson 4) – Form B

Unit 12 Mid-Unit Quiz (Through Lesson 4) – Form C

Unit 12 Mid-Unit Quiz (Through Lesson 4) – Form D

U12.AO.01 – Die Rolling Probability Activity

EDITABLE RESOURCE

U12.AO.02 – Lesson 5.5 Independent Events – Enrichment

U12.AO.03 – Additional Practice with Conditional Probability

U12.AO.04 – More Work with Independence

U12.AO.05 – Practice Using Products to Calculate Probabilities

U12.AO.06 – Practice with Adding Probabilities

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Solutions for Introduction to Probability and Statistics 13th

William mendenhall, robert j. beaver, barbara m. beaver, get access to all of the answers and step-by-step video explanations to this book and 5,000+ more. try numerade free., describing data with graphs.

Describing data with Numerical Measures

Describing Bivariate data

Probability and Probability Distribution

Several useful discrete distributions.

The Normal probability Distribution

Sampling distributions, large-sample estimation, large-sample test of hypotheses, inference from small samples, the analysis of variance, linear regression and correlation, multiple regression analysis, analysis of categorical data, nonparametric statistics.

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Browse Course Material

Course info, instructors.

• Prof. John Tsitsiklis
• Prof. Patrick Jaillet

Departments

• Supplemental Resources

As Taught In

• Systems Engineering
• Probability and Statistics

Learning Resource Types

Introduction to probability, course description.

The tools of probability theory, and of the related field of statistical inference, are the keys for being able to analyze and make sense of data. These tools underlie important advances in many fields, from the basic sciences to engineering and management.

This resource is a companion site to 6.041SC Probabilistic …

This resource is a companion site to 6.041SC Probabilistic Systems Analysis and Applied Probability . It covers the same content, using videos developed for an edX version of the course.

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Statistics 110: Probability

Strategic Practice and Homework Problems

Actively solving practice problems is essential for learning probability. Strategic practice problems are organized by concept, to test and reinforce understanding of that concept.  Homework problems  usually do not say which concepts are involved, and often require combining several concepts. Each of the Strategic Practice documents here contains a set of strategic practice problems, solutions to those problems, a homework assignment, and solutions to the homework assignment. Also included here are the exercises from the  book that are marked with an s, and solutions to those exercises.