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Binomial Probability — result sheet
Exact and cumulative probabilities for a fixed number of independent 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); cumulative sums k terms exactly.
Each trial is independent with the same success chance. Exact integer combination arithmetic keeps small probabilities accurate; cumulative sums use the same exact terms.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Trials (n) — minimum 1; maximum 1000
- Successes (k) — Cannot exceed n.; minimum 0; maximum 1000
- Success probability per trial — %; minimum 0; maximum 100
Worked example
| Input | Value |
|---|---|
| Trials (n) | 10 |
| Successes (k) | 5 |
| Success probability per trial | 50 |
P(X = 5) = 0.2461; P(X <= 5) = 0.6230.
Assumptions and limits
- Independent trials with constant p; 0 <= k <= n <= 1000, integers.
- p entered 0-100 as percentage points.
- Counts must fit safe integers; extreme tails may underflow to 0.
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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