Financial Risk Manager Part 1
Get started today
Ultimate access to all questions.
Deep dive into the quiz with AI chat providers.
We prepare a focused prompt with your quiz and certificate details so each AI can offer a more tailored, in-depth explanation.
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?
Other
Community
NNikitesh
A
15%
B
24%
C
30%
D
33%
Explanation:
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.
Comments
Loading comments...