Answer: 20%

## Explanation To find P(C | M), the probability of a claim given that the policyholder is male, we use the formula for conditional probability: $$ P(C | M) = \frac{P(C \cap M)}{P(M)} $$ Where: - P(C ∩ M) is the joint probability of both a claim and the policyholder being male - P(M) is the marginal probability of the policyholder being male From the table: - P(C ∩ M) = $\frac{100}{1300}$ (100 claims by males out of 1300 total observations) - P(M) = $\frac{500}{1300}$ (500 males out of 1300 total observations) Now calculate the conditional probability: $$ P(C | M) = \frac{P(C \cap M)}{P(M)} = \frac{\frac{100}{1300}}{\frac{500}{1300}} = \frac{100}{500} = 20\% $$ Therefore, the probability that a claim is made given that the policyholder is male is 20%.

Author: Tanishq Prabhu