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A company has two plants to manufacture ...

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

Text Solution

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Let `E_1 " and " E_2` be the events of choosing a bicycle from the first and second plants respectively, then
`P(E_1)=60/100 " and " P(E_2)=40/100=2/5`
let E be the event of choosing a bicycle 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_1|E)` = probability of choosing a bicycle from the first plant, given that it is of standard quality
`=(P(E_1)P(E|E_1))/(P(E_1)P(E|E_1)+P(E_2)P(E|E_2))`
`=(3/5xx4/5)/(3/5xx4/5+2/5xx9/10)=4/7`
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