Conditional Probability

Definition

Basically this is about Probability of one event, IF another event has happened before.

The notation is $P(A|B)$, and can be read as “Probability of A given B has happened before”.

Equation

The equation of such conditional probability is: $P(A|B)=\frac{P(A\cap B)}{P(B)}$ The difference between conditional probability and non-conditional probability is that:

• for denominator: instead of the whole sample size, we use the probability of the “given” event that had happened before i.e. $B$.
• for numerator: instead of only $P(A)$, we use the intersect of events $A$ and $B$, as the intersect lives within the scope of the “given event” which is $B$.

Visually it can be explained with the image below: