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Answer: 24%
This is a Bayes' theorem problem. We need to find P(Standard | Male). **Given:** - P(Male | Standard) = 0.40 - P(Male | Preferred) = 0.50 - P(Male | Ultra Preferred) = 0.75 - P(Standard) = P(Preferred) = P(Ultra Preferred) = 1/3 (equal number in each tier) **Step 1: Calculate P(Male)** P(Male) = P(Male | Standard) × P(Standard) + P(Male | Preferred) × P(Preferred) + P(Male | Ultra Preferred) × P(Ultra Preferred) P(Male) = (0.40 × 1/3) + (0.50 × 1/3) + (0.75 × 1/3) P(Male) = (0.40 + 0.50 + 0.75) × 1/3 P(Male) = 1.65 × 1/3 = 0.55 **Step 2: Apply Bayes' theorem** P(Standard | Male) = [P(Male | Standard) × P(Standard)] / P(Male) P(Standard | Male) = (0.40 × 1/3) / 0.55 P(Standard | Male) = (0.13333) / 0.55 ≈ 0.2424 or 24.24% **Step 3: Interpretation** The probability that a randomly selected male policyholder is from the standard tier is approximately 24%, which corresponds to option B. **Key concepts:** Bayes' theorem, conditional probability, law of total probability.
Author: Nikitesh Somanthe
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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 male policyholder is selected at random, what is the chance he is classified as a standard tier?
A
15%
B
24%
C
30%
D
33%
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