Conditional Probability

Given $A$ and $B$ are events with $P(B)>0$, the conditional probability of $A$ given $B$, denoted by $P(A|B)$, is defined as: $P(A|B)=\frac{P(A\cap B)}{P(B)}$

Context

Conditional probability is foundational in statistics and machine learning. For example, if 30% of emails are spam and 80% of spam emails contain the word “free,” then $P(\text{contains "free"}|\text{spam})=0.80$. Bayes’ theorem builds directly on conditional probability.

See Also

• event
• sample space
• variance