common.theory.example1
\(\text{Coin flips: } n=10, p=0.5, k=7 \rightarrow P(7 \text{ heads}) = 11.72\%\)
Binomial Distribution
Calculate binomial probabilities and cumulative probabilities
Results
Enter values and click Calculate to see the result.
common.theory.binomialDistribution
common.theory.binomialDescription
- common.theory.binomialCondition1
- common.theory.binomialCondition2
- common.theory.binomialCondition3
- common.theory.binomialCondition4
common.theory.keyFormulas:
- common.theory.binomialFormula
- common.theory.meanFormula
- common.theory.varianceFormula
- common.theory.stdDevFormula
common.theory.binomialApplications
\(P(X = k) = C(n, k) \times p^k \times (1-p)^{n-k}, \mu = np, \sigma^2 = np(1-p)\)
Worked Examples
common.theory.example2
\(\text{Quality control: } n=20, p=0.1, k=2 \rightarrow P(2 \text{ defects}) = 28.52\%\)