Question

It is estimated that there are 34 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

Step-by-step explanation:

The probablility of having to pay a death claim on the policy is

`(34)/(10,000,000)`

insurance companys loss = $1 - $100,000 = -$99,999

Consider the outcome in which there is no death claim on the policy.

1 − Probability of death claim = Probability of no death claim

1 -
`(34)/(10,000,000)  = 0.9999966`

If the insurance company does not need to pay a death​ claim, its gain​ is:

Profit − Cost = Gain or Loss

The expected value is calculated by multiplying the gain or loss for each possible outcome by its​ probability, and then adding these products together.

-$99,999
`(34)/(10,000,000)`+$1(0.9999966) = $0.66

Over the long​ run, the insurance company can expect to make ​$0.66 on each policy that it sells.