A particular electronic component is produced at two plants for an electronics manufacturer. Plant A produces 60% of the components used and the remainder are produced by plant B. The proportion of defective components produced at plant A is 1% and the proportion of defective components produced at plant B is 2%. If a component received by the manufacturer is defective, the probability that it was produced at plant A isA. 3/7.

B. 2/7.

C. 4/7. D. 1/7.

Question

Mathematics

River Tran

26 June, 02:22

A particular electronic component is produced at two plants for an electronics manufacturer. Plant A produces 60% of the components used and the remainder are produced by plant B. The proportion of defective components produced at plant A is 1% and the proportion of defective components produced at plant B is 2%. If a component received by the manufacturer is defective, the probability that it was produced at plant A isA. 3/7.

B. 2/7.

C. 4/7. D. 1/7.

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Answers (1)

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Porter Leach · Answer 1

A) 3/7

Step-by-step explanation:

We start by calculating the following probabilities:

P (produced by A) = 0.6

P (produced by A and defective) = P (A ∩ def) = 0.6*0.01 = 0.006

P (produced by A and not defective) = P (A ∩ not def) = 0.6*0.99 = 0.594

P (produced by B and defective) = P (B ∩ def) = 0.4*0.02 = 0.008

P (produced by B and not defective) = P (B ∩ not def) = 0.4*0.98 = 0.392

The probability that it was produced by A given that it is defective is:

P (A|def) = P (A ∩ def) / P (def) = P (A ∩ def) / (P (A ∩ def) + P (B ∩ def)) = 0.006 / (0.006+0.008) = 6/14 = 3/7