The binomial distribution gives the discrete probability distribution P_{p}(k|N) of obtaining exactly k successes out of N trials where the result of each trial is true with a probability of p and false with a probability of q = 1 − p.

P_{p}(k|n) = \binom{N}{k}p^{k}q^{N−k},  (1)
= \frac{N!}{k!(N − k)!}p^{k}(1 − p)^{N−k},  (2)

where \binom{N}{n} is a binomial coefficient.

We can find P = “the probability that 10 or less users are active.” Then 1 − P = “ the probability that more than 10 users are active.” We find P as

∑_{k=0}^{10} \binom{35}{k}p^{k}q^{N−k}  (3)