In general for N total balls (N>1): Pr(R,R) = 2 / ( (N+1) (N) (N-1) ) * N^3 / 3 The N^3 / 3 is just the integral of N^2 evaluated from 0 to N. As N gets larg

In general for N total balls (N>1): Pr(R,R) = 2 / ( (N+1) (N) (N-1) ) * N^3 / 3 The N^3 / 3 is just the integral of N^2 evaluated from 0 to N. As N gets large, then Pr(R,R) approaches (2/3) because the cubic terms in numerator and denominator cancel out. This means that no matter what N is, probability of red,red will always be greater than probability of red,green.