Problem preview

S-MD.7 Warmup M3-055-A04-V02

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

Compare expected value and defined downside-risk metrics

Problem

Return A is \(10\%\) for certain. Return B is \(-40\%\) with probability \(0.20\) and \(+22.5\%\) otherwise. Compute both expected values, then compare loss chance, worst return, and spread.

Answer choices

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Treat B's 22.5% gain as its EV; call B higher-return and lower-risk despite its .20 chance of -40%.

Both have EV 10%, but B has a .20 loss chance, worst return -40%, and greater spread; A is certain.

Compute both EVs as 10%, but call risk equal despite A's certainty and B's .20 loss chance and -40% worst return.

Compute both EVs as 10%, but assign A the .20 loss chance and call A riskier than B.

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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