Financial Risk Manager Part 1
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A company insures both male and female drivers. At the moment, the company has insured an equal number of male and female drivers. Males have a 0.15 chance of having a claim during a policy period while females have a 0.10 chance of having a claim. If a driver is randomly selected from the population, what is the probability that the driver has no claim during the policy period?
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A
73.5%
B
76.5%
C
77.5%
D
87.5%
Explanation:
Explanation
This problem uses conditional probability and the law of total probability to find the probability of no claim.
Given:
- P(Male) = 50% = 0.50
- P(Female) = 50% = 0.50
- P(Claim | Male) = 0.15
- P(Claim | Female) = 0.10
Step 1: Calculate probability of claim using law of total probability [P(Claim) = P(Claim | Male) \times P(Male) + P(Claim | Female) \times P(Female)] [P(Claim) = (0.15 \times 0.50) + (0.10 \times 0.50)] [P(Claim) = 0.075 + 0.05 = 0.125]
Step 2: Calculate probability of no claim [P(No\ Claim) = 1 - P(Claim) = 1 - 0.125 = 0.875] [P(No\ Claim) = 87.5%]
Verification:
- Probability of male with no claim: (1 - 0.15) × 0.50 = 0.85 × 0.50 = 0.425
- Probability of female with no claim: (1 - 0.10) × 0.50 = 0.90 × 0.50 = 0.450
- Total probability of no claim: 0.425 + 0.450 = 0.875 = 87.5%
Both methods confirm that the correct answer is 87.5%.
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