1.8 Dependent Events and Conditional Probability

When the outcome of the previous event affects the outcome of the subsequent event, they are called Dependent events. Say, drawing a queen card from a deck of playing cards after removing one card (and not putting it back) is a dependent event. Dependent events can lead to Conditional Probability.

Conditional probability is one of the most fundamental concepts in probability and machine learning because it allows us to understand the relationship between two or more events. If events are correlated, the occurrence of one event can influence the probability of another event. It addresses the question “What is the probability of an event occurring, given that another event has already occurred?”.

When we condition an event A on another event B, we enter the universe where B has already occurred. It implies that the only outcomes now possible are the ones that are part of B. In other words, the sample space gets reduced to B (Fig 1.18).