Statistics and Probability Dictionary
Select a term from the dropdown text box. The online statistics
glossary will display a definition, plus links to other
related web pages.
Binomial probability refers to the probability that a
results in exactly x successes.
The following notation is helpful when we talk about binomial probability.
x: The number of successes that result from the binomial experiment.
n: The number of trials in the binomial experiment.
p: The probability of success on an individual trial.
q: The probability of failure on an individual trial. (This is equal to
1 - p.)
b(x; n, p): Binomial probability - the probability that an n-trial
binomial experiment results in exactly x successes, when the
probability of success on an individual trial is p.
nCr: The number of
of n things, taken r at a time.
Given x, n, and p, we can compute the binomial probability
based on the following formula:
Suppose a binomial
experiment consists of n
trials and results in x
the probability of success on an individual trial is p
, then the
binomial probability is:
b(x; n, p)
= nCx * px * qn - x