If the probablity of products produced by machine A,B,C is 0.4 , 0.2 ,0.6 and th

Question

If the probablity of products produced by machine A,B,C is 0.4 , 0.2 ,0.6 and the probability of deflect of each machine is p(d|a A) = 0.03 , p(d|B) = 0.04 , p(d|C) = 0.05. What is the probability of a product selected at random and it it deflected ? If the probablity of products produced by machine A,B,C is 0.4 , 0.2 ,0.6 and the probability of deflect of each machine is p(d|a A) = 0.03 , p(d|B) = 0.04 , p(d|C) = 0.05. What is the probability of a product selected at random and it it deflected ? A) = 0.03 , p(d|B) = 0.04 , p(d|C) = 0.05. What is the probability of a product selected at random and it it deflected ?

Explanation / Answer

Let defected event be denoted by D.

P(D | A) = 0.03

P(D | B) = 0.04

P(D | C) = 0.05

Using the total probability theorem:

P(D) = P(D | A)*P(A) + P(D | B)*P(B) + P(D | C)*P(C)

= 0.03*0.4 + 0.04*0.2 + 0.05*0.6 = 0.05

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