What type of probability refers to the likelihood of one event occurring given that another event has occurred?

The concept of conditional probability is central to understanding how events relate to one another in probability theory. Conditional probability refers specifically to the likelihood of one event occurring given that another event has already occurred. This relationship is expressed mathematically as P(A|B), which denotes the probability of event A occurring under the condition that event B has occurred.

This concept is critical in various fields, including healthcare statistics, where understanding the relationship between different events—such as the occurrence of a disease given certain risk factors—can inform clinical decisions and public health policies. By using conditional probability, we can make more accurate predictions and better understand the dependencies between different events in our data.

In contrast, the other types of probabilities mentioned do not focus on this conditional relationship. Addition probability pertains to the likelihood of either of two events occurring, joint probability combines the probabilities of two events happening together, and marginal probability considers the probability of an event without regard for other related events. Understanding these distinctions helps clarify the unique role that conditional probability plays in statistical analysis.