17 An insurer classifies flood hazard based on geographical

17. An insurer classifies flood hazard based on geographical areas, with hazard categorized as low, medium and high. The probability of a flood occurring in a year in each of the three areas is Area Hazard low medium high Prob. of Flood .001 .02 .25 The insurer\'s portfolio of policies consists of a large number of policies with 80% low hazard policies, 18% medium hazard policies and 2% high hazard policies. Suppose that a policy had a flood claim during a year. Find the probability that it is a high hazard policy. A) .50 B) .53 C) .56 D) .59 E) .62

Solution

Probability of flood claim (low) = 0.001

Probability of flood claim (med) = 0.02

Probability of flood claim (high) = 0.25

Policy claim with flood = (P(high) * Probaility that the policy is high one)/(P(high) * Probaility that the policy is high one + P(low) * Probaility that the policy is low one + P(med) * Probaility that the policy is med one)

= (0.02 * 0.25)/(0.001*80 + 0.02*0.18 + 0.02 * 0.25)

= 0.53191

Hence the correct answer is option B