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Question

In a bolt factory, machines A,B and C manufacture 25%,35% and 40% respectively of the total number of bolts. The percentage of defective bolts among the manufactured bolts is 5% for A , 4% for B and 2% for C. A bolt is drawn randomly from the manufactured products and is found to be defective then,

A
the probability that the selected bolt is defective =0.0345
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B
the probability that the defective bolt was manufactured by machine A=2569
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C
the probability that the defective bolt was manufactured by machine B=2869
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D
the probability that the defective bolt was manufactured by machine C=1669
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Solution

The correct options are
A the probability that the selected bolt is defective =0.0345
B the probability that the defective bolt was manufactured by machine C=1669
C the probability that the defective bolt was manufactured by machine A=2569
D the probability that the defective bolt was manufactured by machine B=2869
Let X be the event that a defective bolt is manufactured.
P(X)=0.25×0.05+0.35×0.04+0.40×0.02=0.0345
P(A|X)=0.25×0.050.0345=2569
P(B|X)=0.35×0.040.0345=2869
P(C|X)=0.40×0.020.0345=1669

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