MathLiveBinomial probability mass function
Gives the probability of observing exactly x successes in n independent trials, each with success probability p. It is used for counting successes in a fixed number of yes/no experiments.
P(X = x) = \binom{n}{x} p^x (1 - p)^{n - x}What the symbols mean
| discrete random variable counting the number of successes | |
| number of successes observed, an integer from 0 to n | |
| number of independent trials | |
| probability of success on each trial, between 0 and 1 | |
| binomial coefficient, the number of ways to choose x successes among n trials |
About this formula
- FieldMathematics
- TopicProbability distributions
- LevelUniversity
- Also calledbinomial distribution formula, binomial probability formula, probability of k successes in n trials, binomial pmf, bernoulli trials probability, binomial coefficient probability
- SourceWikidata Q185547
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