Suppose we are interested in two events, A and B. In this case, event A might represent the event that a patient has appendicitis and event B might represent a patient having a high white blood cell count. The conditional probability of event A given event B is essentially the probability that event A will occur when we know that event B has already happened.
Formally, we define the conditional probability of event A given event B as the joint probability of both events occurring divided by the probability of event B occurring:
Note that this is consistent with the way in which we define statistical independence. Statistical independence ...