question_answer 1)

A manufacturer has three machines operators A, B and C. The first operator A produces 1% defective items whereas the other two operators B and C produces 5% and 7% defective items respectively. A is one 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 A? 

Answer:

Let E1, E2 and E3 be the events of selection of operators A, B and C respectively and F  = event of getting defective item.                               Required probability = (E1/F) =