# Binomial distribution

Is quite easy to understand. What I don't understand though is this:
When you sum over all the binomial probabilities from i=0 to n you should get 1, as this corresponds to the total probability of getting any outcome. I just don't understand what it is, that guarantees that you always get one when you sum over:
Ʃ(p)i(1-p)n-i$\cdot$K(n,i)
Why is this sum always equal to 1?

straight out of the binomial theorem,$$\sum_{i=0}^n {\binom n i} p^i (1-p)^{n-i} = (p + (1-p))^n = 1^n = 1$$