Problem

Payoff A is $\$5$ for certain. Payoff B is $\$100$ with probability $0.05$ and $\$0$ otherwise. Compute both expected values, then compare downside and spread.

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What this problem is really about

Expected value compresses a payoff distribution into one average, so equal averages can hide very different experiences. After computing each mean, return to the actual outcomes and measure downside relative to the stated benchmark, along with the worst outcome and overall spread. Those are separate facts; an overall preference requires a stated attitude toward risk.

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Compute both EVs as $5, but assign A the .95 below-$5 chance and call A riskier than B.

Both have EV $5, but A has no downside and zero spread while B is below $5 with probability .95 and has much greater spread.

Compute both EVs as $5, but call risk equal despite A's zero spread and B's .95 chance of paying below $5.

Treat B's $100 maximum as its expected value; call B higher-return and lower-risk, with no downside despite its .95 chance of $0.

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Payoff A is \(\$5\) for certain. Payoff B is \(\$100\) with probability \(0.05\) and \(\$0\) otherwise. Compute both expected values, then compare downside and spread.

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