Financial Risk Manager Part 1
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55% of an insurer's policyholders are male and 45% are female. The chance of a male having a claim is 10% and the chance of a female having a claim is 7%. Given a randomly selected policyholder has a claim, what's the probability she is a female?
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A
25%
B
33%
C
36%
D
38%
Explanation:
This question makes use of Bayes' theorem. We know that: P(M) = 0.55 and P(F) = 0.45
Also, P(C|M) = 0.10 and P(C|F) = 0.07
Now, we need P(F|C). Using Bayes' Theorem,
P(F|C) = \frac{P(C|F) \cdot P(F)}{P(C|F) \cdot P(F) + P(C|M) \cdot P(M)}
= \frac{0.07 \times 0.45}{0.07 \times 0.45 + 0.10 \times 0.55}
= \frac{0.0315}{0.0865}
= 0.3642 ≈ 36%
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