Math 2.0

Probability theory and stochastic processes Definition

Classical definition of probability

Builds on Probability spaceFinite set

Definition

Let Ω\Omega be a nonempty finite set of equally likely outcomes. The classical probability of an event A⊆ΩA \subseteq \Omega is P(A)=∣A∣∣Ω∣,P(A) = \frac{|A|}{|\Omega|}, the number of favourable outcomes divided by the number of all outcomes.

Remarks

This PP is a probability measure on the power set of Ω\Omega, the uniform probability on Ω\Omega. Each outcome has probability 1/∣Ω∣1/|\Omega|. For two rolls of a fair die, the probability that the sum is 77 is 6/36=1/66/36 = 1/6. Classical probability turns a probability problem into a counting problem. Binomial coefficients and the rule of product often give the counts. The definition is circular as a foundation, since "equally likely" already uses probability. It also does not apply to infinite sample spaces.

Reading path

To understand this page from the ground up, read these 41 pages in order. The foundations come first.

  1. Construction of the reals from Cauchy sequences concept
  2. Element definition
  3. Integers object
  4. Ordered field definition
  5. Proposition concept
  6. Random experiment concept
  7. Rational numbers object
  8. Set definition
  9. Ring of integers statement
  10. Disjunction definition
  11. Implication definition
  12. Predicate definition
  13. Ordered pair definition
  14. Union definition
  15. Sample space definition
  16. The rationals form a field statement
  17. Existential quantifier definition
  18. Universal quantifier definition
  19. Cartesian product definition
  20. Subset definition
  21. The rationals form an ordered field statement
  22. Uniqueness quantifier definition
  23. Binary relation definition
  24. Universal set definition
  25. Order on the reals definition
  26. Power set definition
  27. Complement definition
  28. Function definition
  29. Interval definition
  30. Codomain definition
  31. Injective function definition
  32. Sigma-algebra definition
  33. Surjective function definition
  34. Event definition
  35. Bijective function definition
  36. Probability axioms concept
  37. Equinumerous sets definition
  38. Probability measure definition
  39. Finite set definition
  40. Probability space definition
  41. Classical definition of probability definition

Where this leads

5 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Classical_definition_of_probability, lead section
About this page
Tag0AKNPYQ04R
URIm2://0AKNPYQ04R
Aliasesuniform-probability-on-a-finite-set
Kinddefinition
WritingW0 stub
MSC60A05
DefinesClassical definition of probability
UsesProbability space, Finite set

Markdown · JSON · Edit on GitHub

What this page needs for W1

  • an inventory row: the row of the inventory that the node accounts for (0 of 1)

The writing levels say how complete the text of a page is. They do not measure its truth.

What links here

Used by