Probability theory
Binomial distribution
Success-count probabilities, mean and spread in Bernoulli trials.
Probability theory
Binomial probability of k successes
P(X=k)=Cₙᵏpᵏ(1−p)ⁿ⁻ᵏ→Probability theoryBinomial probability of zero successes
P(X=0)=(1−p)ⁿ→Probability theoryBinomial: at least one success
P(X≥1)=1−(1−p)ⁿ→Probability theoryBinomial probability up to k
P(X≤k)=ΣCₙⁱpⁱ(1−p)ⁿ⁻ⁱ→Probability theoryBinomial mean
μ=np→Probability theoryBinomial standard deviation
σ=√(np(1−p))→