Statistics
Binomial Probability Calculator
Use this binomial calculator when each trial has the same success probability and trials are independent.
P(X = k)
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- Combinations
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- Expected successes
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the binomial probability calculator solves
Use this binomial calculator when each trial has the same success probability and trials are independent.
Formula
How to use it
- Enter number of trials.
- Enter exact successes.
- Enter success probability as a percent.
How to read the answer
The result is the probability of exactly k successes, not at least k successes.
Common mistakes and edge cases
- Trials must be independent.
- Success probability must stay the same each trial.
- Exact and cumulative probabilities answer different questions.
Worked examples
Exactly 3 successes
P(X = k)
21.4991%
Coin-flip style
P(X = k)
27.3438%
Frequently asked questions
What does exact probability mean?+
It means exactly k successes, not fewer, more, or at least k.
What if trials are not independent?+
Then the binomial model may not fit; use a model that matches the sampling process.
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Last updated: May 15, 2026