Q. 114.0( 4 Votes )

An insurance company insured 3000 scooters, 4000 cars and 5000 trucks. The probabilities of the accident involving a scooter, a car and a truck are 0.02, 0.03 and 0.04 respectively. One of the insured vehicles meet with and accident. Find the probability that it is a (i) scooter (ii) car (iii) truck.

Answer :

Given:


Company has 3000 scooters, 4000 cars and 5000 trucks.


Let us assume U1, U2, U3 and A be the events as follows:


U1 = choosing scooter


U2 = choosing car


U3 = choosing truck


A = Involving in accident





From the problem:


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



P(A|U2) = P(car involving in a accident)



P(A|U3) = P(truck involving in accident)



Now we find


P(U1|A) = P(The vehicle which met with accident is a scooter)


P(U2|A) = P(The vehicle which met with accident is a car)


P(U3|A) = P(The vehicle which met with accident is a truck)


Using Baye’s theorem:

















The required probabilities are .


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