Binomial probability

n trials, p success → P(exactly k), P(≤k), P(≥k)

Parameters

P(X=k) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ — the model for 'k successes in n independent trials': coin flips, defects on a line, click conversion. Expectation E = n·p, σ = √(n·p·(1−p)). Example: P(exactly 3 heads in 10) = 11.7%.

Probabilities

P(X = k)
11.72%
P(X ≤ k)
17.19%
P(X ≥ k)
94.53%
E = n·p
5.00
σ
1.581