How to use the binomial probability calculator
Find the probability of k successes in n trials. Enter trials, successes, success probability in the fields above; the p(x = k), mean, standard deviation are computed instantly and plotted on the chart so you can see how the answer changes.
Formula
Variables
- n — Trials
- k — Successes
- p — Success probability
Worked example
With trials = 10, successes = 3, success probability = 0.5, the calculator gives p(x = k) ≈ 0.1171875; mean ≈ 5; standard deviation ≈ 1.581139.
Frequently asked questions
What is the formula for the binomial probability calculation?
P(X = k) = nCr(n,k) × p^k × (1-p)^(n-k). Mean = n × p. Standard deviation = √(n × p × (1-p)). Here n is trials, k is successes, p is success probability.
What inputs do I need for the binomial probability calculator?
You need trials, successes, success probability. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use this calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.