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SigmaCalc
The math behind coin flips, quality-control sampling, and any process with a fixed 'success or not' probability per trial.
It requires a fixed number of independent trials, each with only two possible outcomes, and the same success probability every time — think repeated coin flips, not something where the odds change as you go.
This calculator gives P(X = k), the probability of exactly that many successes. To find P(X ≤ k) or P(X ≥ k), you'd sum this formula across the relevant range of k values.
P(X = k)
0.205
P(X = k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ
What you entered
Number of ways to choose k successes
C(10, 4)= 210Probability of that exact sequence
0.5^4 × (1 − 0.5)^6= 0.001P(X = k)
210 × 0.001= 0.2051Result
P(X = k): 0.205
Out of 10 independent trials with a 50% success probability, there's a 20.51% chance of exactly 4 successes.