BinomialDistribution

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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!     p   q

X! (N-X)!

DickBeldin----

If you go to previous versions and look at the first one, 02/15/2001, which is yours?, you will see :

1). q (1-p), maybe a typo?

2). And the formula for the numbers of ways of picking X items out of N items was:

N!/X!/(N-X)!. This is plain wrong. Yes, after requesting a change for a week, I changed it.

3).There were also wording problems. RoseParks.