# Math Help - Proof that binomial function is a probability function?

1. ## Proof that binomial function is a probability function?

How can I prove that the binomial function is a probability function?

I attached the solution I got from my slides...but I dont understand the 2nd part!

2. ## Re: Proof that binomial function is a probability function?

Originally Posted by Marmy
How can I prove that the binomial function is a probability function?
I attached the solution I got from my slides...but I dont understand the 2nd part!
The binomial probability is $P(X=k)=\binom{N}{k}p^kq^{N-k}$ where $q=1-p$

Thus, $1 = \left( {p + q} \right)^N = \sum\limits_{k = 0}^N {\binom{N}{k}p^k q^{N - k} }$

Thanks!