It is estimated that there are 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.

Question

It is estimated that there are  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.

GPT 3.5 · Answer

To calculate the expected value, we multiply the probability of each outcome by the associated payout and sum them up.

Let's assume the probability of death in a plane crash is x out of 10 million. Therefore, the probability of surviving is (10,000,000 - x) out of 10 million.

The expected value for each policy can be calculated as follows:
Expected Value = (Probability of death * Payout in case of death) + (Probability of survival * Payout in case of survival)

Expected Value = (x/10,000,000) * $100,000 + ((10,000,000 - x)/10,000,000) * $0

Simplifying the equation, we get:
Expected Value = $100,000 * (x/10,000,000)

Since a policy can be purchased for $1, the insurance company's profit per policy sold is:
Profit per Policy = Expected Value - Policy Cost
Profit per Policy = $100,000 * (x/10,000,000) - $1

Therefore, the insurance company can make $100,000 * (x/10,000,000) - $1 in the long run for each policy sold.