winds

05-31-2010, 10:32 PM

I read this as a solution to a problem, but I'm not sure how to get it:

Say we have k balls, of which 1 is red and k-1 are black, and k is odd. If we split them into two "half" piles of m and n balls, with m = n + 1, then the probability that pile "m" will have the red ball is m / (m+n).

I understand the other part, when k is even, then probability is 0.5, because it's equally likely to end up in either pile. And I understand, in the odd case, that the probability will be greater for the bigger "m" pile. But why will it be exactly the ratio given above?

Any insight much appreciated. Thanks.

Say we have k balls, of which 1 is red and k-1 are black, and k is odd. If we split them into two "half" piles of m and n balls, with m = n + 1, then the probability that pile "m" will have the red ball is m / (m+n).

I understand the other part, when k is even, then probability is 0.5, because it's equally likely to end up in either pile. And I understand, in the odd case, that the probability will be greater for the bigger "m" pile. But why will it be exactly the ratio given above?

Any insight much appreciated. Thanks.