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Question

A company has two plants to manufacture bicycles. The first plant manufactures 60% of the bicycles and the second plant 40%. Out of the 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.

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Solution

Let A, E1 and E2 denote the events that the cycle is of standard quality, plant I is chosen and plant II is chosen, respectively.

PE1=60100 PE2=40100 Now, PA/E1=80100PA/E2=90100Using Bayes' theorem, we getRequired probability = PE2/A=PE2PA/E2PE1PA/E1+ PE2PA/E2+PE3PA/E3 =40100×9010060100×80100+40100×90100 =3648+36=3684=37


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