Questions 41-45 are based on the following information: Machine A produces 3% de

Question

Questions 41-45 are based on the following information: Machine A produces 3% detectives, Machine B produces 5% defectives, and Machine C produces 10% detectives. Of the total output from these machines, 50% of the items are from Machine A, 30% from B, and 20% from C. What is the probability 41. One item is selected at random from a day's production. that the item came from Machine C? A. 0.03 B. 0.05 C. 0.10 D. 0.20 42. One item is selected at random from a day's production. that the item is defective? What is the probability A. 0.03 B. 0.05 C. 0.10 D. 0.20 43. If inspection finds the item to be defective, what is the revised probability that the item came from Machine A? A. 0.1 B. 0.2 C. 0.3 D. 0.4 44. If inspection finds the item to be defective, what is the revised probability that the item came from Machine B? A. 0.1 B. 0.2 C. 0.3 D. 0.4 45. If inspection finds the item to be defective, what is the revised probability that the item came from Machine C? A. 0.1 B. 0.2 C. 0.3 D. 0.4

Explanation / Answer

Given P(A) = 0.50, P(B) = 0.30, P(C) = 0.20
P(D/A) = 0.03, P(D/B) = 0.05, P(D/C) = 0.10 where D is defectives

41. P(C) = 0.20
Correct answer: Option (D)

42. P(D) = P(A)*P(D/A) + P(B)*P(D/B) + P(C)*P(D/C)
= 0.50*0.03 + 0.30*0.05 + 0.20*0.10 = 0.05
Corect answer: option (B)

43. P(A/D) = P(D/A) P(A) / P(D)  
= 0.03*0.50 / 0.05 = 0.3
Correct answer: Option (C)

44. P(B/D) = P(D/B) P(B) / P(D)  
= 0.30*0.05 / 0.05 = 0.3
Correct answer: Option (C)

45. P(C/D) = P(D/C) P(C) / P(D)  
= 0.20*0.10 / 0.05 = 0.4
Correct answer: Option (D)

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