Binomial Probability Calculator

P(k of n) = C(n,k)·pᵏ·(1−p)ⁿ⁻ᵏ: count the arrangements, multiply by each arrangement's chance. Six heads in ten fair flips: 210 arrangements × (½)¹⁰ ≈ 20.5%. It governs anything with independent yes/no trials — defect counts, conversion tests, free throws.

'At least k' sums the tail — usually the question people mean ('what are the odds of 6 or more?'). For large n the binomial smooths into the normal curve, which is why polling margins and quality control both lean on z-scores downstream of this formula.