Question

A manufacturer has three machine operators A, B and C. The first operator A productes 1% defective items, whereas 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 on the job for 30% of the time and C on the job for 20% fo the time. A defective item is produced. What is the probability that it was produced by A?

Answer 1

Let E₁ = Product by machine A 

E₂ = Product by machine B 

E₃ = Product by machine C 

Then E₁,E₂ and E₃ are mutually exclusive events