Question 27
Based on historical data, an insurance company estimates that a particular customer has a
3.1% likelihood of having an accident in the next year, with the average insurance payout
being .
If the company charges this customer an annual premium of , what is the company’s
expected value of this insurance policy?

To find the expected value of the insurance policy for the company, we need to calculate the profit or loss based on the potential outcomes and their probabilities. The likelihood of the customer having an accident is 3.1%, which is 0.031 in decimal form, and the payout in case of an accident is $3200. Conversely, if no accident occurs (which has a probability of 96.9% or 0.969), the company keeps the entire premium of $310.

The expected value can be calculated as follows:

Calculating each part:

Now, summing these two values:

Therefore, the company’s expected value from this insurance policy is approximately $210.80. This means the insurance company can reasonably expect to make about $210.80 on this customer after accounting for the likelihood of an accident and the associated costs.