CCSS.Math.Content.HSS-MD.B.5
The standard
(+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
Common Core State Standards for Mathematics
What this standard means
Students need to list possible outcomes for a choice, attach a probability to each outcome, and assign a payoff value, often money, points, or utility. Then they multiply each payoff by its probability and add the products to find the expected value.
Mastery means students can compare two or more options using expected value and explain which choice is better under the model. They also know a high expected value does not guarantee a good result every time. Common trouble spots are using percentages as whole numbers, missing outcomes, and treating expected value as the most likely outcome.
Ways to teach it
- Have students build a simple spinner game with paper clips, assign prize values, and calculate whether the game is fair.
- Ask students to write which is better, a guaranteed $20 or a 25% chance at $100, and justify with expected value.
- Give a two-row payoff table and ask students to find the expected value and choose the better option in three minutes.
- Compare phone insurance plans by listing repair costs, estimated probabilities, premiums, and expected yearly cost.
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Related standards
- CCSS.Math.Content.HSS-MD.B
Use probability to evaluate outcomes of decisions
- CCSS.Math.Content.HSS-MD.B.6
(+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
- CCSS.Math.Content.HSS-MD.B.5b
Evaluate and compare strategies on the basis of expected values.
- CCSS.Math.Content.HSS-MD.B.5a
Find the expected payoff for a game of chance.