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?
Other
Community
NNikitesh
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,
Explanation: This is a classic application of Bayes' Theorem for conditional probability. We want to find the probability that a policyholder is female given that they have a claim (P(F|C)). Using Bayes' Theorem, we calculate the numerator as the probability of having a claim given female (0.07) times the probability of being female (0.45), which equals 0.0315. The denominator is the total probability of having a claim, which is the sum of: (probability of claim given female × probability of female) + (probability of claim given male × probability of male) = (0.07 × 0.45) + (0.10 × 0.55) = 0.0315 + 0.055 = 0.0865. Dividing 0.0315 by 0.0865 gives approximately 0.3642 or 36%.
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