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