Question

You just bought a smartphone for $300, and upon checkout, you are asked if you'd like to purchase a one-year "accidental damage" insurance policy, for "only $48". The policy will pay you $300 to replace the phone if it breaks for any reason. If you estimate that your probability of damaging your phone in the next year is about 6% (based of course on googling up some actual statistics, rather than just making up numbers), what is the expected value of purchasing this policy?

Hint: find the expected value of the payout, and subtract the cost of the policy.

Answer 1

Cost of Smart Phone	$        300
Cost of Insurance Policy for 1 year	$          48
Probability of damaging phone in next year	6%
Amount of Claim in case of damage	$        300
Expected value of Payout = $ 300 * 6%	$          18
Less: Cost of Policy	$          48
Expected Value of Purchasing this Policy	$        (30)