Let A be the probability that some station can successfully transmit in a slot .
we know C= 1/A where C = Number of Contention Intervals
Given that , A=K*p* (1-p)k-1 ...(i) where K= no. of station, and p=probability
In (i) value of A is maximum when p=1/K
Thus A = (1-1/K)K -1
so maximum value of A is (1-1/K)K -1 for p = 1/K .