Binomial Point Probability Calculator
Enter integers 0 ≤ n ≤ 10,000 and 0 ≤ x ≤ n, plus decimal probability p from 0 to 1.
A QUICK WALKTHROUGH
How to use this tool
- Enter the trial count n and exact success count x.
- Enter the same success probability p for every trial.
- Calculate P(X = x); review the assumptions and numerical precision.
Formula and source
P(X=x) = C(n,x)p^x(1−p)^(n−x). OpenStax explains the binomial model and its point probability. https://openstax.org/books/introductory-statistics-2e/pages/4-3-binomial-distribution
Scope and precision
The number of trials is fixed; trials are independent, have two outcomes and share constant p. Only the probability of exactly x successes is calculated, without tails or intervals. A compensated sum of logarithms avoids factorial overflow. Results use floating-point arithmetic; extremely small probabilities are shown in scientific notation. p = 0 and p = 1 are handled explicitly; n = 0, x = 0 gives probability 1.
Local calculation
Inputs are processed in this browser without upload or storage.
GOOD TO KNOW
Common questions
Can I enter a percentage?
Convert it to a decimal first: 25% is 0.25.