Question

It is estimated that there are 21 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. The expected value is $1 (Round to the nearest cent.)

Answer 1

$0.79 profit per person who buys a policy

Explanation:

For every 10 million people who buy a policy the expected outcome is

$(21*100,000) = $2,100,000 (21 deaths out of 10 million)

the expected income is

$10,000,000 ($1 per sold policy)

So the expected profit is

$10,000,000 - $2,100,000 = $7,900,000

To obtain how much the insurance company can make for each policy that it sells, we cross multiply

10,000,000 people ---------> $7,900,000 profit

1 person -----------------------> x

and

10,000,000=7,900,000/x and x = $0.79 profit per person who buys a policy