MathematicsHigh School

Binomial and hypergeometric distributions

The model for independent trials

Estimated time · 12 min 9 Content blocks

Core concepts

Formulas

P(X=k)=Cnk pk(1−p)n−k,E(X)=np, D(X)=np(1−p)P(X=k) = \mathrm{C}_n^k\, p^k (1-p)^{n-k},\qquad E(X)=np,\ D(X)=np(1-p)

Formulas

P(X=k)=CMk CN−Mn−kCNnP(X=k) = \frac{\mathrm{C}_M^k\,\mathrm{C}_{N-M}^{n-k}}{\mathrm{C}_N^{n}}

Worked example

Example
Solution

Worked example

Worked examples
Example
Solution steps
  1. 1
  2. 2
  3. 3
Answer

Worked example

Worked examples
Example
Solution steps
  1. 1
  2. 2
  3. 3
Answer

Worked example

Worked examples
Example
Solution steps
  1. 1
  2. 2
  3. 3
Answer
Practice setBinomial distribution practice
Answered 0 / 1
1Fill in the blank
Results are not saved — this session disappears when you leave.

Prerequisites

Numerical characteristics of discrete random variables11 min
AI DO LEARN

Science, made explorable.

5 Disciplines·6 Levels·647 Knowledge points

© 2026 AI DO LEARN. All rights reserved.

Original explanations, diagrams and code may not be republished without permission; please credit the source when quoting.