Conditional probability

When we receive some information about an experiment, the probability we assign to an event can change. Conditional probability formalises this update.

Definition

The conditional probability of $A$ given $B$, with $P(B) > 0$, is: $P(A \mid B) = \frac{P(A \cap B)}{P(B)}.$ It is the probability of $A$ “knowing that” $B$ has occurred: it reduces the universe of outcomes to $B$ and measures the fraction of $B$ that also lies in $A$.

Links

Topics: Probability
Concepts: Probability · Conditional probability
Methods: Conditional prob
Skills: Calculating probability