Q. 105.0( 1 Vote )

# A factory has three machines X,Y and Z producing 1000, 2000 and 3000 bolts per day respectively. The machine X produces 1% defectives bolts, Y produces 1.5% and Z produces 2% defective bolts. At the end of a day, a bolt is drawn at random and is found to be defective. What is the probability that this defective bolt has been produced by machine X?

Given:

Factory X has produced 1000 bolts per day

Factory Y has produced 2000 bolts per day

Factory Z has produced 3000 bolts per day.

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

U1 = choosing factory X

U2 = choosing factory Y

U3 = choosing factory Z

A = choosing a defective bolt

From the problem:

P(A|U1) = P(Choosing defective bolt from factory X)

P(A|U2) = P(Choosing defective bolt from factory Y)

P(A|U3) = P(Choosing defective bolt from factory Z)

Now we find

P(U1|A) = P(The chosen bolt is from factory X)

Using Baye’s theorem:

The required probability is .

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