Statistics Dictionary
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Binomial Probability
Binomial probability refers to the probability that a
binomial experiment
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.)
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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
combinations
of n things, taken r at a time.
Given x, n, and p, we can compute the binomial probability
based on the following formula:
Binomial Formula. Suppose a binomial
experiment consists of
n trials and results in
x successes. If
the probability of success on an individual trial is
p, then the
binomial probability is:
b(x; n, p)
= nCx * px * qn - x
