Before you are three urns. The first two each contain 4 white and 6 black balls. The third has 3 white and 6 black.

Take one ball from the first urn and add it to the second with out looking at it. Stir it in, then take one ball from the second and add it to the third without looking at it.

If you pick a ball from the third urn, what is the probability it will be white?

What is the least number of balls you can put in the urns (at least one black and one white in each) to make the probability at the end equal to exactly 1/3?

A probability of 1/3 can be reached by placing two black and one white ball in each urn.

The four combinations are as follows:

BBW:  6/48
BWW: 4/48
WBW: 2/48
WWW: 4/48

Total probability of drawing white out of Urn 3:

16/48 or 1/3

Posted by hoodat on 2007-02-20 16:45:06