Consider a B(n, p) and a H(A, B, n) where p = A/(A + B)

please derive: the variance of

hypergeometric =n*(AB/((A + B)^2))*(A+B-n)/(A+B-1)

why is binomial variance samallerA+B-n> (A+B-1) ?

since factor (A+B-n)/(A+B-1) is less than 1 ; therefore variance of hypergeometric is smaller)