Conditional probability and Bayes’ theorem

Given two events $A$ and $B$, and considering $P\left(B\right)\ge 0;$, the conditional probability is defined with the following expression:

This definition fulfills the three axioms of the axiomatic definition of probability.

Figure 1 Representation of two events with intersection

$P(A/B)$ can be understood as the probability of the intersection event ($A\cap B$) when event B occurs.

Bayes’ Theorem: The conditional probabilities $P(A/B)$ and $P(B/A)$, can be related with the Bayes Theorem.