Expert: Paul Klarreich - 4/6/2006

Question
Suppose that 35% of a company's television sets are manufactured at a plant in Portland and 65% at a plant in Houston. Of those made in Portland, 2% are defective, and of those made in Houston 6% are defective.
What fraction of their total production is defective?

If you buy a defective set from the company, what is the probability it was made in Houston?

I thought it would be 1/8 for production defective  but that seems incorrect.i know im leaving something out

Answer
Hi, Kevin,
You wrote:
Subject:  Percentages
Question:  Suppose that 35% of a company's television sets are manufactured at a plant in Portland and 65% at a plant in Houston. Of those made in Portland, 2% are defective, and of those made in Houston 6% are defective.
What fraction of their total production is defective?

If you buy a defective set from the company, what is the probability it was made in Houston?

I thought it would be 1/8 for production defective but that seems incorrect.  I know I'm leaving something out.

------------------------------
You have:

0.35 are 'Portland'
0.02(0.35) are 'defective' and 'portland'.

0.65 are 'Houston'
0.06(0.65) and 'd' and 'h'.

So  0.02(0.35) + 0.06(0.65) are defective.
That's  0.007 + 0.039 = 0.046, or  4.6% overall.

If you buy a defective set, your 'sample space' becomes the 0.046.

Since 0.039 of the sets are 'd' and 'h', the probability is 0.039/0.046, or 39/46.