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?

Answer :

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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