Conditional Probability

What is it?

Conditional Probability can be understood as the probability of an event happening, assuming that another event has already happened.

The probability of A, given B, expressed as $P(A|B)$, is the occurrence of event A is conditioned to the previous occurrence of B, which assumes $P(B)>0$. This reduces the sample space for the problem, given that all events in the sample space are equally probable. The conditional probability $P(A|B)$ can be calculated as:

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