What is the probability it came from factory A?

Question

Factories A and B produce computers. Factory A produces 2 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.032 and the probability that an item produced by factory B is defective is 0.021.

A computer is selected at random and it is found to be defective

Answer 1

This can be solved using Bayes Rule, but I think it's more intuitive to use a tree diagram.

Note that since Factory A makes twice as many computers as Factory B, it makes 2/3 of all the computers.

2/3 * .22 = .1467 (defective and produced by A)

/

/

defective .22

/

/ 1/3 * .21 = .07 (defective and produced by B)

A 2/3 /

/ /

Produced by / /defective .21

\ /

\ /

B 1/3

So, the total probability of a defective computer is ]

(defective and produced by A) + (defective and produced by B) = .1467 + .21 = .3567

out of the these, we are interested in the defective produced by B,

which has probability .07 / .3567 = .1962