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the binomial distribution is used to calculate the number of successes in a fixed number of independent trials, each with the same success probability — the classic "how many heads in ten coin flips" problem. It returns the probability of exactly k successes, P(X = k) = C(n, k)·pᵏ·(1 − p)ⁿ⁻ᵏ), along with the cumulative probabilities of at most k and at least k successes. It also reports the distribution’s mean (n·p), variance (n·p·(1 − p)) and standard deviation, and shows the full probability distribution as a table and a chart.The binomial probability calculator uses the binomial distribution to model the number of successes in aWorked example:The term C(n, k) is the number of ways to choose which k of the n trials succeed, pᵏ is the chance those k succeed and (1 − p)ⁿ⁻ᵏ the chance the rest fail. The probability of exactly k successes is C(10, 3) × 0.5³ × 0.5⁷ ≈ 11.7%. The full probability distribution is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The term C(n, k) is 1.Worked example:The