The Baker family is faced with two possible states.In state 1,they remain healthy and incur no medical expenses.In state 2,their medical expenses will be $8,000.There is a 30% chance that state 1 will occur and a 70% chance that state 2 will occur.An insurance company offers to pay all of their medical expenses for a premium of $6,000.From the Bakers' point of view,this is a fair insurance policy.

Question

Quizplus · Accepted Answer

To determine if the insurance policy is fair, we need to compare the expected value of their medical expenses without insurance to the expected value of their medical expenses with insurance.

Without insurance: 
Expected value = (0.3 x $0) + (0.7 x $8,000) = $5,600

With insurance: 
Premium = $6,000 
Expected value = (0.3 x $6,000) + (0.7 x $0) = $1,800

Since the expected value without insurance is higher than the expected value with insurance, the insurance policy is not fair from the Bakers' point of view. They would be paying more in premiums than they would be saving in medical expenses.

The Baker Family Is Faced with Two Possible States