You choose one of two identical looking bags at random. One bag has three black marbles and one white marble. The other has three white marbles and one black marble.

After choosing a bag you draw one marble out at random. You notice it is black. You then put it back and draw another marble out of the same bag at random.

What is the probability that the second marble drawn is black?

I'm not great at probability problems, so I won't be surprised if I am wrong. When I was reading Trevor's solution, I got all confused - so even though my answer is different, I'm definitely not trying to say Trevor is wrong.

That said, I think the answer is 5/16. I kind of read the problem as "given these bags, what is the probability that two black marbles will be pulled in a row?" Already I could be wrong by thinking about it this way.

I saw the answer to this problem as "1/2*(probability of pulling two from Bag 1) + 1/2*(probability of pulling two from Bag 2)" So I calculated 1/2*3/4*3/4 + 1/2*1/4*1/4 = 9/32 + 1/32 = 5/16.

My version of the problem ignores that we know for certain that a black marble was pulled the first time. But then would that make my calculations 1/2*1*3/4 + 1/2*1*1/4 = 3/8 + 1/8 = 1/2? That doesn't make sense to me either.

Please be nice when you tell me what I did wrong =) Thanx!

Posted by nikki on 2003-10-13 15:47:36