1. A factory producing headsets has three assembly lines, A, B, and C, which manufacture 20%, 30%, and 50% of the total production, respectively.

Question

1. A factory producing headsets has three assembly lines, A, B, and C, which manufacture 20%, 30%, and 50% of the total production, respectively. 

It is known that the products from assembly lines A, B, and C are 2%, 1%, and 3% defective, respectively. 

A headset is chosen at random from the output of the factory and is found to be

defective. 

What is the probability that it came from assembly lines A, B, and C?

Answer 1

First we need to find the probability of a headset coming out defective which is the % chance it's made from a certain assembly line * the % chance it is defective and add the outcomes up:

.2*.02+.3*.01+.5*.03=.022

Now we take this as the probability that a headset is defective, and now we put each assembly line in the numerator to find the probability of each:

A) .2*.02/.022=18.18%

B) .3*.01/.022=13.64%

C) .5*.03/.022=68.18%