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 re(3): Have you lost your marbles ? by DJ)

DJ writes: "What you're forgetting this time is that, if you picked a black marble on your first try, either bag is not equally likely...out of 400 trials in which you picked the black marble, 300 of those times you will be holding the bag with three black marbles and one white marble, and you will pull a second black marble 225 times...."

Excellent point, DJ. Good insight into the problem. You are correct. I did overlook that point. Maybe I'll give the flooble website a rest for a while, and stick to brain surgery......nahhhhhhh.... :-)

Posted by Dan on 2003-10-14 00:47:26