Financial Risk Manager Part 1
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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.)
| Male (M) | Female (F) | Total | |
|---|---|---|---|
| Claim (C) | 100 | 200 | 300 |
| No Claim (X) | 400 | 600 | 1000 |
| Total | 500 | 800 | 1300 |
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TTanishq
A
8%
B
10%
C
20%
D
23%
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:
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) = (100 claims by males out of 1300 total observations)
- P(M) = (500 males out of 1300 total observations)
Now calculate the conditional probability:
Therefore, the probability that a claim is made given that the policyholder is male is 20%.
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