1. ## Probability.

Company A produces 60%of the total output and Company B produces the rest(40%). 5% of the goods for Company A and 10% for company B are defects.

If a good is randomly selected what is the chance of it being a defect.

I have P(Defect)= P(Defect A) + P(Defect B)
$=0.6*0.05+0.4*.1=0.07$

If a good is known to be a defect what is the probability it was produced by Company A.

This one I am stuck on, any help would be appreciated

2. Let D = defect.

You want:
P(A|D)
= $P(A union D)/P(D)$
= $(0.6*0.05)/0.07$

3. Originally Posted by actsci231
Let D = defect.

You want:
P(A|D)
= $P(A {\color{red}\cap} D)/P(D)$
= $(0.6*0.05)/0.07$
Small correction in red. The numerical calculation is not affected.

I will also point out that this question is easily done by first drawing a tree diagram. Made by Company A and Made by Company B are the first two branches. Defective and not defective are the next two branches.

4. Alright that makes sense, the probability of Company A defect/ divided by the probability of a defect. Thanks a lot.