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FRM Part I · FRM Exam Part I · Fundamentals of Probability

An insurer finds that 60% of policyholders are urban and 40% rural. The probability of a claim in a year is 10% for urban and 25% for rural policyholders. A policyholder is randomly selected and is known to have made a claim. What is the probability that the policyholder is rural?

The probability that the claimant is rural is 0.625. Total claim probability is 0.06 from urban plus 0.10 from rural, or 0.16. The rural share of that is 0.10 divided by 0.16. The prior of 0.40 must be updated upward because rural policyholders claim more often.

  1. A0.625Correct
  2. B0.400
  3. C0.250
  4. D0.375

Explanation

P(claim) = 0.6×0.10 + 0.4×0.25 = 0.06 + 0.10 = 0.16. P(rural and claim) = 0.10. Bayes gives P(rural | claim) = 0.10 / 0.16 = 0.625. The 0.400 option is the prior probability, ignoring the evidence of a claim.

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