You draw a sea of reds, with blues on the i-th, j-th, and n-th (terminating) draws
1<=i < j < n
Ex: i = 4, j = 10, n = 15: R R R B R R R R R B R R R R B
The probabilitiy of such an string, is:
Conclude that the expectation is .
(I'm going to double check this later - it took too long. However, it looks like a reasonable result.)