Statistics & Probability
Advanced

Binomial Distribution

Probability of k successes in n trials.

Formula

P(X=k)=(nk)pk(1−p)n−kP(X=k) = \binom{n}{k}p^k(1-p)^{n-k}

Variables

nTrials
kSuccesses
pSuccess probability

Example

Flipping 10 fair coins, P(exactly 5 heads) = C(10,5)·0.5¹⁰ ≈ 0.246.

Did You Know?

The binomial distribution models coin flips and quality control — any fixed number of yes/no trials.

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