Question

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.

Answer 1

Answer:

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