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Binomial Distribution Calculator

Online binomial distribution: probability of exactly k successes in n independent trials, with mean np.

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P(X=k)=C(n,k)p^k(1−p)^(n−k)
Trials
0-1
0≤k≤n

📖 Tutorial | Binomial Dist

1. Definition
In n independent trials with success probability p, exactly k successes give P(X=k)=C(n,k)p^k(1−p)^(n−k).
2. Formula & Notation
n,p,kTrials, probability, count
3. Properties & Laws
  • Independent, two outcomes, fixed p;
  • Mean np;
  • Variance np(1−p);
  • Written X~B(n,p).
4. Steps
  1. Enter n,p,k;
  2. Click "Calculate";
  3. Or click "Load Example".
5. Worked Examples
Example: 5 heads in 10 tosses: C(10,5)(0.5)^10≈0.2461, mean 5.
6. Common Pitfalls
Independent trials;
p between 0 and 1;
Exactly, not at most.

❓ FAQ | Binomial Dist

Condition?
Independent, fixed p.
Formula?
C(n,k)p^k(1−p)^(n−k).
Mean?
np.
Variance?
np(1−p).
Example?
0.2461.
At most?
Sum terms.