Financial Risk Manager Part 1
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An insurance company classifies its policyholders into three tiers – standard, preferred, and ultra preferred. 40% of standard tier policyholders are male, 50% of preferred tier policyholders are male and 75% of ultra preferred tier policyholders are male. There is an equal number of policyholders in each tier. If a policyholder is selected at random, what is the chance she is female?
Other
Community
NNikitesh
A
25%
B
30%
C
33%
D
45%
Explanation:
Let event F be "female", event S be "standard", event P be "preferred" and event U be "ultra preferred"
P(F) = P(F|S) * P(S) + P(F|P) * P(P) + P(F|U) * P(U)
P(F) = 0.60 * (1/3) + 0.50 * (1/3) + 0.25 * (1/3)
P(F) = 0.45 or 45%
Explanation:
- Since 40% of standard tier are male, 60% are female → P(F|S) = 0.60
- Since 50% of preferred tier are male, 50% are female → P(F|P) = 0.50
- Since 75% of ultra preferred tier are male, 25% are female → P(F|U) = 0.25
- There are equal numbers in each tier, so P(S) = P(P) = P(U) = 1/3
- Using the law of total probability: P(F) = (0.60 × 1/3) + (0.50 × 1/3) + (0.25 × 1/3) = 0.45 = 45%
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