Calculating Conditional Probability

The calculation of the joint probability of two events works quite well. It answers the question of how likely it is for two independent events to occur concurrently. In the next step, we aim to calculate the conditional probability of an event given that we know another event occurred. This is also known as the posterior probability.

Graphically, the conditional probability is almost the same as the joint probability. The area representing the positive cases is the same. It is the overlap of event $A$ and event $B$, but the base set is different. While we consider all possible cases when calculating the joint probability, we only consider the cases where one event occurred when calculating the conditional probability.

Bayes’ Theorem tells us how to calculate conditional probability. We covered Bayes’ Theorem in-depth in the lesson Bayes’ Theorem Here’sa brief recap so that you don’t need to go too far back.

Bayes’ Theorem describes a way of finding a conditional probability. A conditional probability is a probability of an event (our hypothesis) given the knowledge that another event occurred (our evidence). Bayes tells us we can calculate the conditional probability of $P(Hypothesis|Evidence)$ ...