Problem preview

S-MD.7 Warmup M3-055-A04-V04

Analyze decisions and strategies using probability concepts in more complex settings.

Compare expected value and defined downside-risk metrics

Problem

Contract A pays $\$200$ for certain. Contract B pays $\$1,000$ with probability $0.20$ and $\$0$ otherwise. Compute both expected values, then compare downside and spread.

Answer choices

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Compute both EVs as $200, but assign A the .80 below-$200 chance and call A riskier than B.

Both have EV $200, but B is below $200 with probability .80, can pay $0, and has much greater spread; A is guaranteed.

Treat B's $1000 maximum as its expected value; call B higher-return and lower-risk despite its .80 chance of $0.

Compute both EVs as $200, but call risk equal despite A's guarantee and B's .80 below-$200 chance.

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Curriculum context

Course: Math III
Standard: S-MD.7
Category: Statistics and Probability
Domain: Using Probability to Make Decisions
Objective: Analyze decisions and strategies using probability concepts in more complex settings.
Problem type: Compare expected value and defined downside-risk metrics