Q. 255.0( 1 Vote )

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

Answer :

Given:


Company insured 2000 scooters and 3000 motorcycles


Let us assume U1, U2 and A be the events as follows:


U1 = choosing Scooter


U2 = choosing Motorcycle


A = accident involving vehicle


From the problem




P(A|U1) = P(accident involving scooter)



P(A|U2) = P(accident involving motorcycles)



Now we find


P(U2|A) = P(The vehicle involved in an accident is motorcycle)


Using Baye’s theorem:







The required probability is .


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