In what situations is it used?

Used for defect rate calculations, marketing response rates, game win probability calculations, etc.

Is there a limit on the number of trials?

There is no computational limit, but approximations (like normal approximation) are provided for large values.

What is the relationship with normal distribution?

When the number of trials is large enough, the binomial distribution can be approximated by a normal distribution (central limit theorem).

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Binomial Distribution Calculator

Calculate probability, expected value, and variance for binomial distributions. Determine statistics from the number of trials and success probability.

Number of Trials (n)

Success Probability (p)

Number of Successes (k)

Probability Mass Function (PMF) P(X = 5)

1.97247869

Cumulative Distribution Function (CDF) P(X ≤ 5)

1.00000000

P(X ≥ 5)

0.00000000

Mean E(X) = np

5.0000

Variance Var(X) = np(1-p)

2.5000

Standard Deviation σ

1.5811

Probability Distribution Graph

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How to Use

Step 1

Enter Parameters

Enter the number of trials n and success probability p

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Step 2

Specify Successes

Specify the number of successes k for probability calculation

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Step 3

Check Results

Check probability, expected value, variance, and graphs

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Features

Distribution Graph

Visually display the binomial probability distribution graph

Cumulative Probability

Simultaneously calculate cumulative probabilities like P(X≤k) and P(X≥k)

Statistics Display

Auto-calculate and display expected value, variance, standard deviation, and mode

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FAQ

The distribution of the number of successes k in n trials with success probability p. Coin flipping is a classic example.

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