(MASTERY Problem) Chapter 3 Review Practice Problems, Problem 28: Suppose that i

Question

(MASTERY Problem) Chapter 3 Review Practice Problems, Problem 28: Suppose that in a bolt manufacturing plant, machines A, B, and C manufacture respectively 45%, 25%, and 30% of the bolts. It is observed that the three machines produce, respectively, 5%, 2%, and 3% defective bolts (D). If the bolts produced by these machines are mixed in a well-mixed lot and then a randomly selected bolt is found to be defective, find the probability that the defective bolt is produced by (a) machine A, (b) machine B, and (c) machine C First, what is the marginal probability of producing a defective bolt, P(D) = Now, what are the requested conditional probabilities? (a) PAID)= (b) P(B|D)= (c) P(C | D) =

Explanation / Answer

P(machine A)=0.45

P(machine B)=0.25

P(machine C)=0.30

P(D|A)=0.05

P(D|B)=0.02

P(D|C)=0.03

P(D)=P(D|A)*P(A)+P(D|B)*P(B)+P(D|C)*P(C)=0.45*0.05+0.25*0.02+0.30*0.03=0.0365

a)P(A|D)=P(D|A)*P(A)/P(D)= 0.45*0.05/0.0365=0.6164

b)P(B|D)=P(D|B)*P(B)/P(D)= 0.02*0.25/0.0365=0.13699

c)P(C|D)=P(D|C)*P(C)/P(D)=0.03*0.3/0.0365 =0.2466

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