Conditional probabilities

Link: Probability

Contigency table = table form of Venn diagram

Conditional probabilities formula §

$$P(A\cap B\mid B)=\frac{P(\text{the event will happen})}{P(\text{the event already happened})}$$

Stats notation:

$$P(A\cap B\mid B)=P(A\mid B)=\frac{P(A\cap B)}{P(B)}$$

Many people will use the second notation to avoid the redundancy, however, the former notion helps us get a better understanding of Bayes’ theorem.