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Module 5: Probability and statistics

Topic A: Lesson 1: The general multiplication rule

Learn
Compound probability of independent events
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Independent events example: test taking
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Coin flipping probability
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Dependent probability introduction
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The general multiplication rule
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Practice
Independent probabilityGet 3 of 4 questions to level up!
Probabilities of compound eventsGet 3 of 4 questions to level up!
Dependent probabilityGet 3 of 4 questions to level up!

Topic A: Lesson 2: Counting rules—The fundamental counting principle and permutations

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Count outcomes using tree diagram
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Counting outcomes: flower pots
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Permutation formula
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Zero factorial or 0!
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Possible three letter words
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Ways to arrange colors
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Ways to pick officers
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Practice
The counting principleGet 3 of 4 questions to level up!
PermutationsGet 3 of 4 questions to level up!

Topic A: Lesson 3: Counting rules—Combinations

Learn
Intro to combinations
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Combination formula
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Handshaking combinations
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Combination example: 9 card hands
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Practice
CombinationsGet 3 of 4 questions to level up!
Permutations & combinationsGet 5 of 7 questions to level up!

Topic A: Lesson 4: Using permutations and combinations to compute probabilities

Learn
Getting exactly two heads (combinatorics)
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Exactly three heads in five flips
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Example: Different ways to pick officers
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Example: Combinatorics and probability
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Example: Lottery probability
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Mega millions jackpot probability
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Practice
Probability with permutations and combinationsGet 3 of 4 questions to level up!

Topic B: Lessons 5-6: Discrete random variables

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Random variables
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Discrete and continuous random variables
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Valid discrete probability distribution examples
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Probability with discrete random variable example
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Practice
Probability modelsGet 5 of 7 questions to level up!

Topic B: Lessons 7-8: Expected value

Learn
Mean (expected value) of a discrete random variable
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Expected value (basic)
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Practice
Expected valueGet 5 of 7 questions to level up!

Topic B: Lessons 9-12: Creating probability distributions

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Constructing a probability distribution for random variable
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Probability models example: frozen yogurt
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Practice
Constructing probability distributionsGet 3 of 4 questions to level up!

Topic C: Lessons 13-19: Applications of expected value and probability

Learn
Term life insurance and death probability
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Expected profit from lottery ticket
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Expected value while fishing
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Comparing insurance with expected value
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Practice
Expected value with calculated probabilitiesGet 3 of 4 questions to level up!
Making decisions with expected valuesGet 3 of 4 questions to level up!

About this unit

"In this module, students build on their understanding of probability developed in previous grades. In Topic A the multiplication rule for independent events introduced in Algebra II is generalized to a rule that can be used to calculate probability where two events are not independent. Students are also introduced to three techniques for counting outcomes. Topic B presents information related to random variables and discrete probability distributions. Topic C is a capstone topic for this module, where students use what they have learned about probability and expected value to analyze strategies and make decisions in a variety of contexts." Eureka Math/EngageNY (c) 2015 GreatMinds.org