Conditional Probability

Sometimes the probability of an event occurring changes in light of new information.

We call this the conditional probability.

Given an event $B$, the “updated” probability of the event $A$ in light of this is written as $\mathbb{P}(A|B)$.

We have the formula:

$$ \mathbb{P}(A \mid B) = \frac{ \mathbb{P}(A \cap B)}{\mathbb{P}(B)} $$

Which is defined whenever $ \mathbb{P}(B) \ne 0 $ .