Problem

A warranty costs $\$90$; without it, a $\$300$ repair occurs with probability $0.20$. Compute expected costs, compare them, and state how risk protection can affect preference.

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What this problem is really about

Put the protected and unprotected costs on the same time horizon before comparing them. The unprotected side uses a probability-weighted loss, while the protection price is a certain cost. Any extra expected cost for protection is a risk-transfer price, so the monetary average and the value of limiting a rare large bill should be reported separately.

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Treat uninsured expected cost as the full $300 loss versus $90 for warranty; favor warranty on expectation and risk.

Warranty cost is $90 versus uninsured EV $60, but call the warranty cheaper because its cost is certain; ignore the $30 premium for risk protection.

No warranty has expected cost .20($300) = $60 versus $90, while the warranty limits repair risk; a risk-averse preference may differ.

Use costs $90 and $60, but claim expected cost alone automatically decides risk preference and choose no warranty for everyone.

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A warranty costs \(\$90\); without it, a \(\$300\) repair occurs with probability \(0.20\). Compute expected costs, compare them, and state how risk protection can affect preference.

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