Binomial Calculator
Calculate binomial coefficients (combinations), binomial probabilities, and related statistics.
Calculation Mode
Pascal's Triangle Row 10
1104512021025221012045101
Formulas
Binomial Coefficient
C(n,k) = n! / (k!(n-k)!)
Binomial Probability
P(X=k) = C(n,k) x p^k x (1-p)^(n-k)
Binomial Coefficient C(n,k)
120
Ways to choose 3 from 10
CC(n,k)
120
PP(X=k)
11.7188%
EExpected Value
5.0000
sStd Deviation
1.5811
Distribution Statistics
Expected Value E[X]
5.0000
n x p = 10 x 0.5
Variance Var(X)
2.5000
n x p x (1-p)
About Binomial Distribution
Uses
- Coin flip experiments
- Quality control (defect rates)
- Election polling
- Medical trials
Requirements
- Fixed number of trials (n)
- Two possible outcomes (success/failure)
- Constant probability (p)
- Independent trials