Q. 165.0( 1 Vote )

In a factory, machine A produces 30% of the total output, machine B produces 25% and the machine C produces the remaining output. If defective items produced by machines A, B, C are 1%,1.2%, 2% respectively. Three machines working together produce 10000 items in a day. An item is drawn at random form a day’s output and found to be defective. Find the probability that it was produced by machine B?

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

U1 = choosing Machine A

U2 = choosing Machine B

U3 = choosing Machine C

A = Producing a defective output

From the problem:

P(A|U1) = P(Producing defective output from Machine A)

P(A|U2) = P(Producing defective output from Machine B)

P(A|U3) = P(Producing defective output from Machine C)

Now we find

P(U2|A) = P(The found defective item is produced by Machine B)

Using Baye’s theorem:

The required probability is .

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