Binomial Probability Calculator
Find the probability of exactly, at most or at least k successes in n independent trials.
P(X = 3)
0.1171875 (11.71875%)
- P(X ≤ 3)
- 0.171875 (17.1875%)
- P(X < 3)
- 0.0546875 (5.46875%)
- P(X ≥ 3)
- 0.9453125 (94.53125%)
- P(X > 3)
- 0.828125 (82.8125%)
- Mean and standard deviation
- 5 and 1.58113883
Show the work
Ways to pick the successes
C(n, k) = n! ÷ (k! × (n − k)!)
10! ÷ (3! × 7!) = 120
Chance of exactly 3 successes
P(X = k) = C(n, k) × p to the power of k × (1 − p) to the power of n − k
120 × 0.5 to the power of 3 × 0.5 to the power of 7 = 0.1171875 (11.71875%)
How it works
P(X = k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ; cumulative probabilities add these terms; mean = np, variance = np(1 − p)
Questions
- How does the binomial probability calculator work?
- P(X = k) = C(n, k) pᵏ (1 − p)ⁿ⁻ᵏ; cumulative probabilities add these terms; mean = np, variance = np(1 − p).
- What do I need to enter?
- Trials (n), Success chance (p), Successes (k). Optional fields can be left blank.
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