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?

There are four combinations of choices that will yield a white ball out of urn 3.  The total number of possibilities is found by multiplying the marbles in each urn - 10 * 11 * 10 = 1100

Urn 1:     BLACK   BLACK   WHITE   WHITE
Urn 2:     BLACK   WHITE   BLACK   WHITE
Urn 3:     WHITE   WHITE   WHITE   WHITE

Poss:        126        72          96         80

Probablility = 374/1100 = 34%

Posted by hoodat on 2007-02-20 15:20:10