Answer-first summary for fast verification
Answer: 87.5%
## 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%**.
Author: Tanishq Prabhu
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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?
A
73.5%
B
76.5%
C
77.5%
D
87.5%
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