Question

Annaleigh pays $750 for her yearly car insurance and actuaries determined that she has a 5% chance of being in a car wreck. Actuaries further determined that the insurance company can expect to pay out an average of $5000 per claim. What is the insurance companies expected profit from Annaleigh's policy?​

Answer 1

To calculate the insurance company's expected profit, we need to consider the probability of Annaleigh having a car wreck and the expected payout.

Probability of car wreck: 5% or 0.05
Expected payout per claim: $5000

Expected profit per year = (Probability of wreck) * (Expected payout per claim) - Yearly premium

\[ \text{Expected profit} = (0.05 \times $5000) - $750 \]

Calculate the result to find the expected profit from Annaleigh's policy.