A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by B? A manufacturer knows that the item is defective; even then he sells it in the market. Is he doing the right thing? Which life skill is he lacking?

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

 Let E be the event that the produce item is defective.

P(A) = 50/100 = 0.5, P(B) = 30/100 = 0.3, P(C) = 20/100 = 0.2
P(E | A) = 1/100 = 0.01, P(E | B) = 5/100 = 0.05, P(E | C) = 7/100 = 0.07
Now, B | E be the event that the produced defective item is produced by machine B.
It is not right to sell a defective item in the market. The manufacturer lacks honesty.

Answered by  | 4th Jun, 2014, 03:23: PM