In
probability theory, a
conditional probability measures the
probability of an
event given that (by assumption, presumption, assertion or evidence) another event has occurred. If the event of interest is
A and the event
B is known or assumed to have occurred, "the conditional probability of
A given
B", or "the probability of
A under the condition
B", is usually written as
P(
A|
B), or sometimes
P(
A). For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person has a
cold, then they are much more likely to be coughing. The conditional probability of coughing given that you have a cold might be a much higher 75%.