Q. 175.0( 1 Vote )

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.

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 .

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