Lecture 2 - Ch 4 - Conditional Probability

Given two events, A & B:

the probability of A, given that B has occurred is denoted by P (A|B) and is calculated as:

Intuitively, we understand this as follows:
Look at the Venn diagram in the previous post. Once we know that B has occurred (since that's a given), B is our new sample space. And the only way for A to occur now is
Therefore, the probability of A occurring now is the probability of a successful outcome, i.e. divided by the probability of the entire sample space, i.e.