Binomial Distribution Calculator
Calculate binomial probabilities for experiments with fixed trials and success probability.
Probability
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Enter n, p, and k
P(X = k)
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P(X ≤ k)
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Mean (μ)
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Std Dev (σ)
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Variance
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C(k)
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Binomial Distribution
The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success.
Probability Mass Function
P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
where C(n,k) = n! / (k!(n-k)!) is the binomial coefficient.
Key Formulas
- Mean: μ = np
- Variance: σ² = np(1-p)
- Standard Deviation: σ = √(np(1-p))
Conditions for Binomial
- Fixed number of trials (n)
- Independent trials
- Two possible outcomes (success/failure)
- Constant probability of success (p)