3: Conditional Probability
The probability P ( A ) of an event A is a measure of the likelihood that the event will occur on any trial. Sometimes partial information determines that an event C has occurred. Given this information, it may be necessary to reassign the likelihood for each event A . This leads to the notion of conditional probability. For a fixed conditioning event C , this assignment to all events constitutes a new probability measure which has all the properties of the original probability measure. In addition, because of the way it is derived from the original, the conditional probability measure has a number of special properties which are important in applications.