Naive probability

Source: blitzstein-hwang

Let event $A \subseteq \Omega$ $$ P_\text{naive}(A) = \dfrac{|A|}{|\Omega|} $$ where $|A|$ is the number of elements ( outcomes in $A$).

Required assumptions

• The sample space $\Omega$ is finite.
• The outcomes $\omega \in \Omega$ have equal probability of happening each.

Usage

• Problems with equally likely outcomes.
• Problems with symmetry $\rightarrow$ equally likely probabilities for all outcomes
  e.g. flipping a fair coin
• As a null model (as a hypothesis)