Problem

Minimize expected annual cost subject to worst-case cost at most $\$5,000$. No insurance has a $0.02$ chance of a $\$20,000$ loss; a policy costs $\$600$ plus a $\$2,000$ deductible on a loss. Compute expected and worst-case costs, test eligibility, and recommend.

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No insurance costs $400 expected but has worst case $20000 and is ineligible. The policy costs $640 expected with worst case $2600, so choose the policy.

No insurance has EV cost $400 versus policy $640, so choose no insurance before checking its $20000 worst case against the $5000 limit.

No insurance is ineligible and the policy eligible, but claim the policy has lower expected cost $400 and choose it for the wrong calculation.

No insurance has worst case $20000; call it eligible because variance is absent, then choose it by lower expected cost.

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Minimize expected annual cost subject to worst-case cost at most \(\$5,000\). No insurance has a \(0.02\) chance of a \(\$20,000\) loss; a policy costs \(\$600\) plus a \(\$2,000\) deductible on a loss. Compute expected and worst-case costs, test eligibility, and recommend.

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