Q17 of 249 Page 32

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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