Question

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 1

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|U₁) = 0.01

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

⇒ P(A|U₂) = 0.02

Now we find

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

Using Baye’s theorem:

∴ The required probability is \(\cfrac34.\)