Probability & Combinatorics
Intermediate

Binomial Probability

Probability of k successes in n independent 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

3 heads in 5 flips: C(5,3)(0.5)⁵ = 0.3125

Did You Know?

The binomial distribution models repeated yes/no experiments.

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