A factory has two machines that produce bolts. Machine Iproduces 60% of the dail

Question

A factory has two machines that produce bolts. Machine Iproduces 60% of the daily output of bolts, and 3% of its bolts aredefective. Machine II produces 40% of the daily output, and 2% ofits bolts are defective. (a) What is the probability that a bolt selected atrendom will be defective? (b) If a bolt is selected at random and found to be defective,what is the probability that it was produced by Machine I? A factory has two machines that produce bolts. Machine Iproduces 60% of the daily output of bolts, and 3% of its bolts aredefective. Machine II produces 40% of the daily output, and 2% ofits bolts are defective. (a) What is the probability that a bolt selected atrendom will be defective? (b) If a bolt is selected at random and found to be defective,what is the probability that it was produced by Machine I?

Explanation / Answer

Let A be the event that the bolt is manufactured by Machine 1 and Bbe the event that it is manufactured by Machine 2 Pr(A) = 0.6 and Pr(B) = 0.4 Also Pr(defective/ A) = 0.03 and Pr(defective / B) =0.02; a) Pr(defective) = Pr(A)*Pr(defective/ A) + Pr(B)*Pr(defective /B)---> Law of total probability                         = 0.6*0.03 + 0.4*0.02                         = 0.018 + 0.008                         = 0.026; b) Pr (A/ defective) = Pr (defective given A)* Pr(A) / Pr(defective)                              = 0.03 * 0.6 / 0.026                             = 0.018 / 0.026                               =0.6923

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