Conditional Probability

The probability that event E occurs, given that event F has occurred, is called the conditional probability of event E given event F. In probability notation, it is denoted with p(E|F). Conditional probabilities express the probability of an event (or outcome) under the condition that another event (or outcome) has occurred. You could also think of it as the probability within a particular subset, that is, in the subset of patients with event F in their history, the proportion that develop event E. The conditional probability p(E|F) is the ratio of the joint probability of events E and F, which is denoted as p(E, F) or as p(E and F), and the marginal probability of event F, denoted with p(F):

If the conditional information (“given event ...