There is an 80% probability that Tom will be in good health during the year and incur only $200 in medical expenses, but there is a 20% probability that he will be ill and incur $20,000 in medical expenses. If an insurance company charged Tom an actuarially fair premium, how much would Tom pay for health insurance?

Question

Quizplus · Accepted Answer

The actuarially fair premium is equal to the expected value of Tom's medical expenses. 
Expected Value = (Probability of being in good health x Cost of being in good health) + (Probability of being ill x Cost of being ill)

Expected Value = (0.8 x $200) + (0.2 x $20,000) 
Expected Value = $4,000

Therefore, Tom should pay $4,000 for health insurance, which is option C.

There Is an 80% Probability That Tom Will Be in Good