Question

It is estimated that there are 22 deaths for every 10 million people who use airplanes. A company that sells flight insurance provides​ $100,000 in case of death in a plane crash. A policy can be purchased for​ $1. Calculate the expected value and thereby determine how much the insurance company can make over the long run for each policy that it sells.

Answer 1

Answer:

The insurance company can make $0.78 for each policy that it sells

Step-by-step explanation:

The loss incurred to the insurance company for each death claim is:

$L = \ 1-\ 100,000=-\ 99,999$

This event has a 22 in 10 million probability of happening.

The gain for the company for each policy not claimed is:

$G= \ 1$

This event has a 9,999,978 in 10 million probability of happening.

The expected value is:

$EV =\ 1*\frac{9,999,978}{10,000,000} -\ 99,999*\frac{22}{10,000,000} \\EV=\ 0.78$

Therefore, over the long run, the insurance company can make $0.78 for each policy that it sells.