📊Binomial Distribution Calculator
The binomial distribution models the number of successes in n independent trials with fixed probability p per trial. P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k). Mean = np; variance = np(1−p).
- 1P(X=k) = C(n,k) × pᵏ × (1−p)^(n−k)
- 2C(n,k) = n! / (k! × (n−k)!) — combinations
- 3Applies when: fixed n, binary outcome, constant p, independent trials
Coin flip n=10 · P(exactly 5 heads)=P = C(10,5)×0.5¹⁰ = 24.6%Most likely single outcome, but still only ~25%
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Fun Fact
The binomial distribution approaches the normal distribution as n increases — the Central Limit Theorem in action.
References
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