It is estimated that 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 can make over the long run for each policy it sells.

10 million people = 10 million dollars in revenue

21 deaths = 2.1 million dollars in losses

profit is thus 7.9 million dollars for 10 million policies. That's 79¢/policy

To calculate the expected value, we need to multiply the probability of an event occurring by the value associated with that event, and sum up these values for all possible outcomes.

In this case, the probability of a death in a plane crash is given as 21 deaths per 10 million people who use airplanes. We can convert this probability to a decimal by dividing the number of deaths by the total number of people who use airplanes:

Probability of death = 21/10,000,000 = 0.0000021

The value associated with the event is $100,000, which is the payout in case of death in a plane crash.

Now, let's calculate the expected value using the formula:

Expected Value = Probability x Value

Expected Value = 0.0000021 x $100,000 = $210

Therefore, the expected value of each policy sold is $210.

Now, to determine how much the insurance can make over the long run for each policy it sells, we need to subtract the cost of the policy from the expected value. In this case, the policy can be purchased for $1.

Profit for each policy sold = Expected Value - Policy Cost

Profit for each policy sold = $210 - $1 = $209

So, the insurance can make $209 over the long run for each policy it sells.