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Binomial Probability Calculator — result sheet
Find the probability of exactly k successes in n independent trials with a fixed success probability.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: P(X=k) = C(n,k)pᵏ(1−p)ⁿ⁻ᵏ; expected value = np; standard deviation = √(np(1−p)).
The binomial model describes a fixed number of independent, identically parameterized yes/no trials.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of trials n — minimum 0; maximum 1000
- Successes k — minimum 0; maximum 1000
- Success probability — Enter a decimal from 0 to 1.; minimum 0; maximum 1
Worked example
| Input | Value |
|---|---|
| Number of trials n | 10 |
| Successes k | 4 |
| Success probability | 0.5 |
P(X = 4) ≈ 0.2051; expected value = 5; SD ≈ 1.581.
Assumptions and limits
- Trials are independent and have the same success probability.
- n and k are whole numbers with 0 ≤ k ≤ n.
- The probability is entered as a decimal rather than a percentage.
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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