If you repeat a "yes/no" - experiment $n$ times, and the number of successes is $X$(how often "yes" occurs), then $X$ follows a binomial probability distribution. A binomial experiment therefore consists of $n$ equal and independent experiments, each of which can have exactly two outcomes.
The probability to observe $k$ successes is $\text{P}(X=k)=\left(\begin{array}{c}n\\ k\end{array}\right)\cdot p^k\cdot q^{n-k}$.
In this formula, the chance for "success" is still $p$ and $0\le k\le n$.
The variables $n$ and $p$ are called the parameters of the binomial distribution.

If a statistic is binomially distributed with parameters $n$ en $p$ then the following is true:

• the expected value is: ${\rm E}\left(X\right)=n\cdot p$

Your graphing calculator has two programs for quickly calculating binomial probabilities.
For probabilities of the type ${\rm P}(X=k)$ you should use the binomial probability distribution function.
For probabilities of the type ${\rm P}(X\le k)$ you should use the binomial cumulative distribution function.
Probabilities such as ${\rm P}(X<k),{\rm P}(X>k)$ en ${\rm P}(X\ge k)$ you should convert to the previous form.