BinomialDistribution
:back to ProbabilityDistributions
The Binomial distribution can be described as the sum of a specific number of independent trials, each of which results in either a zero or a one with constant probability. It provides a reasonable description of coin tossing experiments, among others.
To get X heads in a sequence of N tosses, several things have to happen. If the probability of a head on a single trial is p and the probability of a tail is q=(1-p), then each sequence with X heads and N-X tails has a probability calculated by finding the product of multiplying p times itself X times (p^X), and q times itself (N-X) times (q^(N-X)), that is (p^X q^(N-X)). However, there are many sequences which match this description. By the methods of CombinaTorics, we can find that there are N!/(X!*(N-X)!) different combinations with X heads and N-X tails. So, the probability of X heads in N trials is
X (N-X)
N!/(X!*(N-X)!) p q