A company has two plant 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.

Answer

N/a

Explanation

Let `E_(1)=` event that the bicycle is picked up from first plant.
`E_(2)=` event that the bicycle is picked up from second plant.
and `E=` event that the bicycle is of standard quality.
Now `P(E_(1))-60/100,P(E_(2))=40/100`
`P(E//E_(1))=70/100, P(E//E_(2))=80/100`
Now `(E_(2)//E)=` probability that the bicycle is picked up from second plant when it is known that it is of standard quality
`=(P(E_(2)).P(E//E_(2)))/(P(E_(1)).P(E//E_(1))+P(E_(2)).P(E//E_(2)))`
`=(40/100xx80/100)/(60/100xx70/100+40/100xx80/100)`
`=32/(42+32)=32/74=16/37`