This builds on Probability Theory

Conditional Probability

from a joint distribution → if I select yy for YY with P(Y)≠0P(Y)\neq 0

What is the probability xx given yy

P(X∣Y)=P(X,Y)P(Y)\begin{gather*} P(X|Y)=\frac{P(X,Y)}{P(Y)} \end{gather*}

Special case

If X, Y are independent (if X occurs, Y has no effect, and vice versa)

P(X,Y)=P(X)P(Y)\begin{gather*} P(X,Y)=P(X)P(Y) \end{gather*}