Answer-first summary for fast verification
Answer: 45%
## Explanation This is a probability problem using the law of total probability. Let's define the events: - **F**: Female policyholder - **S**: Standard tier - **P**: Preferred tier - **U**: Ultra preferred tier **Given information:** - Equal number of policyholders in each tier: P(S) = P(P) = P(U) = 1/3 - Male percentages: 40% in standard, 50% in preferred, 75% in ultra preferred - Therefore, female percentages: 60% in standard, 50% in preferred, 25% in ultra preferred **Applying the law of total probability:** 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) = (0.60 + 0.50 + 0.25) × (1/3) P(F) = 1.35 × (1/3) P(F) = 0.45 or 45% **Verification:** - Standard tier: 60% female × 1/3 = 20% - Preferred tier: 50% female × 1/3 = 16.67% - Ultra preferred: 25% female × 1/3 = 8.33% - Total: 20% + 16.67% + 8.33% = 45% The correct answer is **45%**, which corresponds to option D.
Author: Tanishq Prabhu
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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?
A
25%
B
30%
C
33%
D
45%
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