A company has two plants to manufacture bicycles. The first plant manufactures 60% of the bicycles and the second plant 40%. Out of that 80% of the bicycles are rated of standard quality at the first plant and 90% of standard quality at the second plant. A bicycle is picked up at random and found to be standard quality. Find the probability that it comes from the second plant.

Question

Philoid · Accepted Answer

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

U₁ = Choosing first plant to manufacture bicycles

U₂ = choosing second plant to manufacture bicycles

A = Picking standard quality cycle

From the Problem

⇒

⇒ P(A|U₁) = P(Picking standard quality cycle from first plant)

⇒

⇒ P(A|U₂) = P(Picking standard quality cycle from second plant)

⇒

Now we find

P(U₂|A) = P(The chosen standard quality cycle is from second plant)

Using Baye’s theorem:

⇒

∴ The required probability is .