Question

"A bicycle factory runs two assembly​ lines, A and B. 95​% of line​ A's products pass inspection and 93​% of line​ B's products pass inspection. 60​% of the​ factory's bikes come off assembly line B and the rest come off line A. Find the probability that one of the​ factory's bikes did not pass inspection and came off assembly line Upper A."

Answer 1

0.02

Explanation:

Since 60​% of the​ factory's bikes come off assembly line B, Therefore:

The probability that the​ factory's bikes come off assembly line B = 60% = 0.6

Percentage line​ B's products pass inspection = 93% = 0.93

Percentage line​ B's products that do not pass inspection = 1 - 0.93 = 0.07

The probability that the​ factory's bikes come off assembly line A = 1 - 0.6 = 0.4

Percentage line​ A's products pass inspection = 95% = 0.95

Percentage line​ A's products that do not pass inspection = 1 - 0.95 = 0.05

Let D represent those that passes inspection and D' represent those that do not pass inspection.

P(A ∩ D') = P(A) × P(D'/A) = 0.4 × 0.05 = 0.02

P()bikes did not pass inspection and came off assembly line A) = P(A ∩ D') = 0.02