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Question

In a toy-making factory, machines A, B and C manufacture 25%, 35% and 40% of the total toys respectively. Of their output, 5% 4% and 2% respectively are defective toys. A toy is drawn at random from the product. If the toy drawn is found to be defective, what is the probability that it is manufactured by the machine B?

A
1769
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B
2869
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C
3569
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D
None of these
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Solution

The correct option is B 2869
Let E1,E2,E3 and A be the events defined as follows:
E1 = the toy is manufactured by machine A
E2 = the toy is manufactured by machine B
E3 = the toy is manufactured by machine C
A = the toy is defective
Then P(E1) = probability that the toy drawn is manufactured by machine A = 25100
Similarly, P(E2)=35100 and P(E3)=40100
P(AE1) = probability that the toy drawn is defective given that it is manufactured by machine A = 5100
Similarly P(AE2)=4100,P(AE3)=2100
Now, required probability
=P(E2)P(AE2)P(E1)P(AE1)+P(E2)P(AE2)+P(E3)P(AE3)
=35100×410025100×5100+35100×4100+40100×2100=2869

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