# ALEX Classroom Resource

## Precalculus and Advanced Topics, Module 5, Topic C: Using Probability to Make Decisions

Classroom Resource Information

Title:

Precalculus and Advanced Topics, Module 5, Topic C: Using Probability to Make Decisions

URL:

Content Source:

EngageNY
Type: Lesson/Unit Plan

Overview:

Module 5, 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 (S.MD.B.5a, S.MD.B.5b, S.MD.B.6, S.MD.B.7). Students use probabilities to make a fair decision and explain how to make fair an “unfair” decision. Students analyze simple games of chance as they calculate and interpret the expected payoff in context. They make decisions based on expected values in problems with business, medical, and other contexts. They also examine and interpret what it means for a game to be fair. Interpretation and explanations of expected values are important outcomes for Topic C.

Note: This module is identified as Precalculus and Advanced Topics in the EngageNY curriculum. It also corresponds to the Algebra II and Algebra II with Trigonometry Alabama Courses of Study.

Content Standard(s):
 Mathematics MA2015 (2016) Grade: 9-12 Algebra II 37 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] Mathematics MA2015 (2016) Grade: 9-12 Algebra II 38 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 41 ) (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [S-MD6] Mathematics MA2015 (2016) Grade: 9-12 Algebra II with Trigonometry 42 ) (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). [S-MD7] Mathematics MA2015 (2016) Grade: 9-12 Precalculus 54 ) (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values. [S-MD5] a. Find the expected payoff for a game of chance. [S-MD5a] Examples: Find the expected winnings from a state lottery ticket or a game at a fast-food restaurant. b. Evaluate and compare strategies on the basis of expected values. [S-MD5b] Example: Compare a high-deductible versus a low-deductible automobile insurance policy using various, but reasonable, chances of having a minor or a major accident.
Tags: expected value, expected values, fair decision, payoff values, probability
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