# 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.

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 .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses