1.

A company has two plants to manufacturebicycles. The first plant manufacture 60% of the bicycles and the second plant, 40%. Also, 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 of standard quality. Find the probability that it comes from the second plant.

Answer»

Solution :Let `E_1 and E_2` be the events of CHOOSING a BICYCLE from the first plant and the second plant respectively. Then,
`P(E_1)=60/100=3/5,and P(E_2)=40/100=2/5`.
Let E be the event of choosing a biacycle of standard quality. Then,
`P(E//E_1)`= PROBABILITY of choosing a bicycle of standard quality, given that it is PRODUCED by the first plant
`=80/100=4/5`.
`P(E//E_2)`=probability of choosing a bicycle of standard quality, given that it is produced by the second plant
`=90/100=9/10`.
The required probability
`P(E//E_2)` =probability of choosing a biacycle from the second plant, given 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))`[by Bayes's theorem]
`((2/5xx9/10))/((3/5xx4/5)+(2/5xx9/10))=3/47`.


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