You do some research and find for a driver of your age and gender the probability of having an accident that results in damage to your automobile exceeding $100 is 1/10 per year. Your auto insurance company will reduce your annual premium by $40 if you will increase your collision deductible from $100 to $250. Should you? Explain.
What will be an ideal response?
An increase of a deductible from $100 to $250 exposes you to an out-of-pocket possible loss of $150 when you have an accident. But the chances of incurring this out-of-pocket loss is 1/10 (0.10) each year, so we can calculate the expected loss as E.L. = 0.1($150) + 0.9($0) = $15.00. Since this expected loss is less than the $40 in premium savings it makes good sense to increase the deductible.
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