"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."

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raphealnwobi raphealnwobi · Answer 1 · 2020-04-22T06:21:03+02:00

Answer:

0.02

Step-by-step 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