A bicycle factory runs two assembly lines A and B 96 of line

A bicycle factory runs two assembly lines, A and B. 96% of line A\'s products pass inspection and 91% of line B\'s products pass inspection. 50% 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 passed inspection and came off assembly line Upper A.

Solution

Here I used the fact by taking the number of bikes to solve the probability..

Say the factory produces 200 bikes.
Since A and B produce 50% of the bikes each,
then A made 100 bikes (of which 96 pass inspection) and B made 100 bikes (of which 91 passed inspection).

So out of the 200 bikes from the factory, 91 of them came from B AND passed inspection: 91/200 =
= 0.455 or 45.5%.