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?

(In reply to Could be wrong by nikki)

You are right in saying that your "version of the problem ignores that we know for certain that a black marble was pulled the first time." What you have calculated is the probability of getting two black marbles from all possible outcomes.

However, since we are told that the first martble was black, the outcomes for which the first marble was white are eliminated, and we need to find the fraction of outcomes just from the cases where the first draw was black.

As it turns out, there is a 50/50 chance that the first marble was either black or white, and with replacement, the two pulls are independent of each other, so your answer is exactly half of what we are looking for.

Posted by DJ on 2003-10-13 16:00:08