Question

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?

Answer 1

Step-by-step explanation:

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