Question

An insurance company sells two types of auto insurance policies: Basic and Deluxe. The time until the next Basic Policy claim is an exponential random variable with mean two days. The time until the next Deluxe Policy claim is an independent exponential random variable with mean three days.

What is the probability that the next claim will be a Deluxe Policy claim?

Answer 1

The probability that the next claim will be a Deluxe Policy claim is lower than the probability that the next claim will be a Basic Policy claim.

Step-by-step explanation:

The probability that the next claim will be a Deluxe Policy claim can be found by comparing the average times until the next claim for the Basic Policy and the Deluxe Policy. The time until the next Basic Policy claim is an exponential random variable with mean two days, while the time until the next Deluxe Policy claim is an independent exponential random variable with mean three days. Since the Deluxe Policy claim has a longer mean time until the next claim, it is less likely to occur compared to the Basic Policy claim. Therefore, the probability that the next claim will be a Deluxe Policy claim is lower than the probability that the next claim will be a Basic Policy claim.