What type of probability is defined as the probability that one event will occur given that another event has occurred?

The type of probability that describes the likelihood of one event occurring given that another event has already occurred is known as conditional probability. This concept is foundational in statistics and probability theory, as it allows us to understand how the probability of an event can change based on the occurrence of another event.

In practical terms, conditional probability is often denoted as P(A | B), which is read as "the probability of A given B." This notation illustrates that the probability of event A depends on the knowledge that event B has already taken place. This is particularly useful in healthcare statistics, where the occurrence of a particular condition or outcome (event A) can depend on the presence of risk factors or other conditions (event B), thus influencing clinical decisions, risk assessments, and treatment plans.

This concept is distinct from other types of probabilities, such as joint probability, which considers the likelihood of two events happening simultaneously, or marginal probability, which looks at the probability of an event without regard to the occurrence of other events. Understanding conditional probability is essential for analyzing dependent events and making informed predictions based on existing evidence in various fields, including healthcare.