Probability Question In a certain assembly plant three machi

Probability Question:

In a certain assembly plant, three machines (B1, B2, and B3) make 30%, 45%, and 25%, respectively, of the products. It is known from past experiences that 2%, 3%, and 2% of the products made by each machine, respectively, are defective. Now, a finished product is selected at random. What is the probability that it is defective?

In the previous problem, if a product is chosen randomly and found to be defective, what is the probability that it was made by machine B3?

Solution

A)

Let

D = defective

Thus,

P(D) = P(B1) P(D|B1) + P(B2) P(D|B2) + P(B3) P(D|B3)

P(D)= 0.30*0.02+0.45*0.03+0.25*0.02 = 0.0245 [ANSWER]

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B)

P(B3|D) = P(B3) P(D|B3) / P(D) = 0.25*0.02/0.0245

= 0.204081633 [ANSWER]