Interpretations
===============

Bayesian interpretation
-----------------------

* Probability measures a *degree of belief*.
* For proposition A and evidence B,

  * P(A), the *prior*, is the initial degree of belief in A.
  * P(A|B), the *posterior*, is the degree of belief having accounted for B.
  * the quotient P(B|A)/P(B) represents the support B provides for A.

Frequentist interpretation
--------------------------

* Probability measures a *proportion of outcomes*.
* For example, suppose an experiment is performed many times.

  * P(A), the proportion of outcomes with property A.
  * P(B), that with property B.
  * P(B|A), the proportion of outcomes with property B *out of* outcomes with property A.
  * P(A|B), the proportion of those with A *out of* those with B.