Calculate probabilities for independent binary trials.
Distribution Parameters
Probability breakdown
Exactly k successes P(X=k) (k=5)24.6094%0.24609375
P(X ≤ k) Cumulative62.30%
P(X ≥ k) At Least62.30%
Mean (μ)5.00
Variance (σ²)2.500
Std Dev (σ)1.581
Probability Distribution
About this calculator
Overview
The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
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Pro Tips
Trials must be independent (one trial doesn't affect another).
Each trial must have exactly two outcomes: success or failure.
k must be an integer between 0 and n.
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Fun Facts
"As the number of trials increases, the binomial distribution starts to look like a normal (bell-shaped) curve."
"A Galton Board is a physical device that demonstrates the binomial distribution by dropping balls through pins."
"The binomial distribution is often used in quality control to estimate the number of defective items in a batch."
