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.

Question

Philoid · Accepted 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 .