Statistics and Probability 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.)
  • 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


See also:   Statistics Tutorial: Binomial Probability | Binomial Calculator