Question

Eleven percent of the pens made by Apex are defective.

Only 6% of the pens made by its competitor, B-ink, are defective. Since Apex pens are cheaper than B-ink pens, an office orders 67% of its stock from Apex and 33% from B-ink. A pen is chosen at random and found to be defective. What is the probability that it was produced by Apex?

Answer 1

Let A be the event 'made by Apex and defective':
P(A) = 0.67 x 0.11 = 0.0737
Let B be the event 'made by B-ink and defective':
P(B) = 0.33 x 0.06 = 0.0198
Let C be the event 'made by Apex or B-ink and defective':
P(C) = P(A) + P(B) = 0.0737 + 0.0198 = 0.0935
P(defective and made by Apex) = 0.0737/0.0935 = 0.788
The answer is 0.788 or 78.8%.