Q:

Conditional Probability - Cell Phone Problem

The screens used for a certain type of cell phone are manufactured by 3 companies, A, B. and C. The proportions of screens supplied by A. B. and C are 0.5, 0.3, and 0.2. respectively, and their screens are defective with probabilities 0.01, 0.02, and 0.03, respectively. Given that the screen on such a phone is defective, what is the probability that Company A manufactured it?
Would it be that: 
P(A) = 1/2 because 0.5 of the screens are made by Company A
and
P(B) = 1/100 because its defective 0.01 of the time?

A:

Hint. The probability that a screen is defective is
$$P(D)=0.5\cdot 0.01+0.3\cdot 0.02+0.2\cdot 0.03=0.017.$$
The probability that a screen is made by Company A and it defective is
$$P(A\cap D)=0.5\cdot 0.01=0.005.$$
Are you able to determine $P(A|D)$?

