CA Foundation · Quantitative Aptitude · Probability
An insurance company classifies drivers as low-risk, medium-risk and high-risk in the proportions 50%, 30% and 20%. The probabilities of at least one claim in a year are 0.02, 0.05 and 0.10 respectively. A policyholder makes at least one claim this year. What is the probability that the policyholder is high-risk?
The probability is 20/45, which equals 4/9. The claim-making shares are 0.010 for low-risk, 0.015 for medium-risk and 0.020 for high-risk drivers, totalling 0.045. High-risk drivers account for 0.020 of that total, giving 4/9.
- A20/45Correct
- B10/45
- C20/100
- D15/45
Explanation
Joint probabilities: low = 0.5 x 0.02 = 0.010; medium = 0.3 x 0.05 = 0.015; high = 0.2 x 0.10 = 0.020. Total = 0.045. P(high | claim) = 0.020/0.045 = 20/45 = 4/9. The option 15/45 is the medium-risk posterior, and 20/100 is just the prior.
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