Question

The probability that a homeowners policyholder reports both a property claim and a liability claim in year 1 is 0.01. The event that a homeowners policyholder reports a property claim is independent of the event that the policyholder reports a liability claim. Calculate the probability that a homeowners policyholder reports both a property claim and a liability claim in year 9.

A) 0.01
B) 0.25
C) 0.001
D) 0.99

Answer 1

The probability of a homeowners policyholder reporting both a property claim and a liability claim in year 9 is 0.0001.

Step-by-step explanation:

To calculate the probability that a homeowners policyholder reports both a property claim and a liability claim in year 9, we need to use the fact that the events are independent. Since the probability of reporting both types of claims in year 1 is 0.01, we can assume the same probability for year 9.

Probability of reporting both claims in year 9:

P(A and B) = P(A) * P(B) = 0.01 * 0.01 = 0.0001

Therefore, the probability that a homeowners policyholder reports both a property claim and a liability claim in year 9 is 0.0001.