People in a certain group have a 0.60 % chance of dying this year. If a person in this group buys a life insurance policy for $5500 that pays $1,000,000 to her family if she dies this year and $0 otherwise, what is the expected value of the policy?

The expected value is calculated by using the probability of each event. If the chance of dying is 0.60% then the chance living is 99.40%. The expect value formula is:

∑[ (xi) * P (xi) ] (for all i events).

In this problem we have two events: live or die. If the person dies the family receives $1,000,000 (X1=$1,000,000) and if the person lives the family receives $0 (X2=$0). The probability of receiving $1,000,000 is 60% (P (x1) = 0.006) and the probability of receiving $0 is 99.40% (P (x2) = 0.994)

Using the formula the expected value of the policy (without the insurance cost):

$1,000,000 * (0.006) + $0 * (0,994) = $6,000

If we subtract the insurance value:

$6,000-$5,500 = $500