Question

In a factory which manufactures bolts, machines A. B and C manufacture respectively 25%, 35% and 40% of the bolts. Of their outputs, 5, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by the machine B? Select the correct answer from above options

Answer 1

let D be the event of defective P(A)=0.25 P(B)=0.35 P(C))=0.4 P(D∣A)=0.05 P(D∣B)=0.04 P(D∣C)=0.02 P(B∣D)= P(D∣B)P(B) P(D∣A)P(A)+P(D∣B)P(B)+P(D∣C)P(C) = 0.04⋅0.35 0.05⋅0.25+0.04⋅0.35+0.02⋅0.4 = 4⋅7 25+28+16 = 28 69 Answer