Binomial Distribution Probability Calculator
Local ProcessingCalculate probability of exactly k successes in n independent Bernoulli trials with probability p.
How It Works & Processing Standards
Enter values above to calculate results automatically. Check each input field for guidance and units.
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P(X = k) = nCk · p^k · (1 − p)^(n − k). Choose general binomial or coin flips (p = 0.5) under "Calculation".
What You Can Do
- Binomial probability
- The chance of exactly k successes in n trials with success probability p
- Coin flips
- The chance of exactly that many heads with a fair coin
How to Use Binomial Distribution Probability Calculator
- 1Choose a calculationBinomial for general trials, coin flips for a fair coin.
- 2Enter countsn (trials), k (successes), p (0 to 1).
- 3Read the resultThe probability is shown as a percentage.
Examples
Exactly 3 of 10 (p = 0.5)
Input: n 10, k 3, p 0.5
Result: 11.71875%
5 heads in 5 flips
Input: Flips 5, heads 5
Result: 3.125%
Common Use Cases
- The chance that k of n products are defective
- Guessing k questions right on a test
- Coin and game probability problems
Frequently Asked Questions (FAQ)
What about "at least k"?
This gives exactly k. For at least k, add the results from k to n.
Is p a percentage?
Enter a decimal from 0 to 1. 30% is 0.3.