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Binomial Exact Probability Calculator — result sheet
Calculate the probability of exactly k successes in n independent Bernoulli trials.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=k)=C(n,k)p^k(1−p)^(n−k).
The exact-success probability is calculated under independent equal-probability trials.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of trials — minimum 0; maximum 1000
- Success probability — minimum 0; maximum 1
- Exact successes — minimum 0; maximum 1000
Worked example
| Input | Value |
|---|---|
| Number of trials | 10 |
| Success probability | 0.4 |
| Exact successes | 3 |
P(X=3)≈21.47%.
Assumptions and limits
- Trial count and success count are whole numbers with successes no greater than trials.
- Trials are independent and share the same success probability.
- Dependence, changing probabilities, sampling without replacement, and decision costs are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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