Calculadora de Distribuição Binomial
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
P = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ
About this calculator
The Binomial Distribution Calculator computes the probability of getting exactly k successes in n independent trials, each with success probability p. The formula used is P(X = k) = C(n,k) · pᵏ · (1−p)ⁿ⁻ᵏ, where C(n,k) is the binomial coefficient. This tool is useful for scenarios with binary outcomes, such as heads/tails, pass/fail, or success/failure.
To use the calculator, enter the number of trials (n), the desired number of successes (k), and the probability of success per trial (p). The result is the exact probability of exactly k successes. For example, when flipping a coin 10 times, what is the chance of exactly 5 heads? Simply enter n=10, k=5, and p=0.5.
This calculator is widely used in quality control, survey analysis, biology, and finance. For instance, to calculate the probability that 3 out of 10 products in a batch are defective, given a defect rate of 2%. Note: trials must be independent and probability p constant. Also, this calculator gives exact k probabilities; for cumulative probabilities, use the cumulative binomial distribution calculator.
Frequently asked questions
What does the binomial coefficient C(n,k) mean?
C(n,k) represents the number of ways to choose k successes from n trials, ignoring order. It is calculated as n! / (k! · (n−k)!).
Can I use this calculator for cumulative probabilities?
No, this calculator only gives the exact probability for a specific k. For cumulative probabilities (P(X ≤ k) or P(X ≥ k)), use the cumulative binomial distribution calculator.
What are the conditions for using the binomial distribution?
The conditions are: fixed number of trials n, independent trials, only two possible outcomes (success/failure), and constant probability p across all trials.
What if the number of trials is very large?
For large n, the calculator may struggle with factorials. In that case, consider approximations like the normal distribution (if np and n(1-p) are greater than 5) or Poisson (if p is small).
Can the probability p be greater than 1?
No, p must be between 0 and 1. Values outside this range are not probabilistic and the calculator will return an error.