Binomial Probability Calculator

Formula

The formula to calculate binomial probability is:

\[ P(X = k) = \binom{n}{k} p^k (1-p)^{n-k} \]

Where:

\( P(X = k) \) is the probability of getting exactly \( k \) successes in \( n \) trials.
\( \binom{n}{k} \) is the number of combinations (n choose k).
\( p \) is the probability of success on a single trial.
\( n \) is the total number of trials.
\( k \) is the number of successes.

Example

Let's say the number of trials is 10, the number of successes is 3, and the probability of success on a single trial is 0.5. Using the formula:

\[ P(X = 3) = \binom{10}{3} 0.5^3 (1-0.5)^{10-3} \approx 0.117 \]

So, the binomial probability is approximately 0.117.

What is Binomial Probability?

Binomial probability is the probability of achieving a specific number of successes in a fixed number of independent trials, with the same probability of success on each trial[^1^][^2^].