Question

Suppose a homcowner spends $300 for a home insurance policy that will pay out $200,000 if the horne is destroyed by fire in a given year. Let Pa the profit made by the company on a single policy. From previous data, the probability that a home in this arca will be destroyed by fire is 0.0002. Here is a table of the probability distribution of P

Profit. $300. -199,700

Probability. 0.998. 0.0002


What is the expected value of P?————(Do not round)
Explain what this result means for the insurance company

If—————- are insured by this company, the —————- amount the company would
make, per home, would be about—————

Answer 1

The expected value of P is $259.46, which means the insurance company expects to make an average profit of $259.46 per policy, per year.

Step-by-step explanation:

The expected value of P, the profit made by the insurance company on a single policy, can be calculated using the formula for expected value, which is the sum of each profit outcome multiplied by its probability. In this scenario, there are two possible outcomes: making a $300 profit (with a probability of 0.998) or taking a $199,700 loss (with a probability of 0.0002). The calculation is:

• (Profit of $300 × Probability of 0.998) = $299.40
• (Loss of $199,700 × Probability of 0.0002) = -$39.94

We then add these two values to find the expected value of P:

$299.40 - $39.94 = $259.46

This result means that the insurance company expects to make an average profit of $259.46 per policy, per year. If many homes are insured, this is the average amount the company would expect to make per home, assuming the risk probabilities remain constant over time.