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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. |
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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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