Statistics

Binomial Distribution Calculator

Find P(exactly k successes) in n trials.

Calculated Output

P(X = k) (%) 11.719

Expected successes 5

Formula: P = C(n,k) pᵏ (1−p)ⁿ⁻ᵏ

Step-by-Step Breakdown

1. Values used:

2. Trials (n) = 10

3. Successes (k) = 3

4. Success probability = 0.5

6. P(X = k) = 11.719%

7. Expected successes = 5

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The math behind it

P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ. Expected value = n × p.

10 trials, k 3, p 0.5 → 11.7%.

Coin flips?

Use p = 0.5 — it's a special case.