Given the following chart describing the claims of an auto insurer during a policy period, calculate P(C|M). (Assume that the number of male and female claims are independent of each other.)

Exam-Like

Community

TTanishq

Explanation:

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%.

Powered ByGPT-5