An insurance company offers car policies to individuals with two different characteristics. Those with characteristic of...

An insurance company offers car policies to individuals with two different characteristics. Those with characteristic of type A will make a claim with probability p1 and those with the characteristic of type B will make a claim with probability p2, where p1 =/= p2. The fraction of the policyholders that are classed as type 1 characteristic is a and those of type 2 is 1−a, where 0 < a < 1. A policyholder is chosen at random. Let Ai denotes the event that this policyholder will make a claim in year i. Assume that A1 and A2 are conditionally independent events on the event the individual has type A characteristics. Further assume that A1 and A2 are conditionally independent events on the event the individual has type B characteristics. p1 and p2 are independant.

1. Show that P(A2 | A1) > P(A1).

2. Provide a brief (one sentence) interpretation of this result.

Expert Solution

Here we have used the theorem of conditional probability, and theorem of total probability or the conditional probability with partition of the sample space.

orchestra answered 2 years ago

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