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Question

An insurance company insured 2000 scooters and 3000 motor cycles. The probability of an accident involving a scooter is 0.01 and that of a motor cycle is 0.02. An insured vehicle met with an accident. Find the probability that the accidented vehicle was a motor cycle.

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Solution

P(E1)=20005000=0.4P(E2)=30005000=0.6P(AE1)=0.01P(AE2)=0.02P(E2A)=P(E1)P(AE2)P(E1)P(AE1)+P(E2)P(AE2)=0.6×0.020.6×0.02+0.4×0.01=0.0120.012+0.004=34

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