Problem preview

S-MD.7 Warmup M3-055-A04-V03

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

Compare expected value and defined downside-risk metrics

Problem

A game pays $+\$3$ with probability $0.99$ and $-\$200$ with probability $0.01$. Compute expected value and assess loss probability, worst outcome, spread, and downside.

Answer choices

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Compute EV as $0.97, but call downside zero because winning probability is .99 and ignore the possible -$200 loss.

Its EV is $0.97, but it has a 1% chance of losing $200 and substantial spread: positive EV does not remove severe downside.

Compute EV as $0.97 and loss chance 1%, but call spread zero because EV is near zero and classify the game as safe.

Compute EV as negative merely because loss is possible; still note a 1% chance of -$200 and call the game unfavorable with high spread.

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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