Two marbles are to be picked from an urn with B>0 blue and R>0 red marbles without replacement.

The probability both picked marbles are the same color is exactly 1/2.
What is can be said about B and R?

Suppose, in addition to the blue and red marbles there is also a single green marble.

The probability both picked marbles are the same color is exactly 1/2.
What is can be said about B and R?

(In reply to

Analytic and computer solutions by Larry)

Something was lost in the first line of Larry's otherwise correct solution.

It should start out with:

b(b-1)/(b+r)(b+r-1) **+ r(r-1)/(b+r)(b+r-1**) = 1/2

The second line, which is correct, follows from this.

2*(b(b-1) + r(r-1)) = (b+r)(b+r-1)