For p ≤ 0.5
There are tables in most formulae books or in the back of a statistics text book that allow you to calculate some Binomial probabilities with ease. This is outlined in the following tutorial.
For p > 0.5
There are tables in most formulae books or in the back of a statistics text book that allow you to calculate some Binomial probabilities with ease. However, sometimes the tables only give values of p up to 0.5.
This tutorial explains how to use the tables still when p>0.5.