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?

If the bag you picked was the one with three white marbles and one black marble, there is zero probability of drawing another black marble. If the bag is the one which originally had three black marbles and one white marble, it now has two black marbles and one white marble, and you have a 2-in-3 (66%) chance of drawing another black marble. There is a 50% chance of drawing either bag. So the probability of drawing the black marble as a second marble is 50% of 66%, or 33%.

Posted by Dan on 2003-10-13 20:43:39