A manufacturer has three machine operators A,B and C. The first operator A produces 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% of the time. A defective item is produced. What is the probability that it was produced by A?

Question

Philoid · Accepted Answer

Let us assume U₁, U₂, U₃ and A be the events as follows:

U₁ = choosing Operator A

U₂ = choosing Operator B

U₃ = choosing Operator C

A = Producing defective item

From the problem:

⇒

⇒ P(A|U₁) = P(Producing defective item by operator A)

⇒

⇒ P(A|U₂) = P(Producing defective item by operator B)

⇒

⇒ P(A|U₃) = P(Producing defective item by operator C)

⇒

Now we find

P(U₁|A) = P(The defective item is produced by operator A)

Using Baye’s theorem:

⇒

∴ The required probability is .