Binomial Probability
Free Binomial Probability calculator with clear step-by-step results.
About Binomial Probability
The binomial distribution gives the probability of exactly k successes.
Formula
Formula
P(X=k) = C(n,k)·p^k·(1−p)^(n−k)
Worked example
With the default values below, Binomial Probability returns P(X = k) of 0.205078. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Number of trials nminimum 1
- 10
- Successes kminimum 0
- 4
- Success probability paccepts 0–1
- 0.5
Results
- P(X = k)
- 0.205078
- Expected Value (np)
- 5.000
- Variance np(1−p)
- 2.500
Step by step
- 1Values used
- 2Formula
- 3P(X = k)= 0.205078
- 4Expected Value (np)= 5.000
- 5Variance np(1−p)= 2.500
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
The binomial distribution gives the probability of exactly k successes.
Why does this matter?
Trials must be independent with constant p.