## Summary of Terms Used in Probability

Two events A and B are mutually exclusive if they cannot both occur, either at the same time, or one after the other, depending on the circumstances. If they are mutually exclusive and  and are the probabilities of events A, B or both A and B occurring respectively, then A and B are mutually exclusive if The definition extends naturally to sets. Two sets A and B are mutually exclusive if or There is no intersection. Events A and B are mutually exhaustive if either A must occur or B must occur or both. This then means that If events A and B are mutually exhaustive then This definition also extends naturally to sets. If sets A and B are mutually exhaustive then or If A and B are also mutually exclusinve then Events A and B are independent if event A does not affect the probability of event B and vice versa.  and satisfy the equation Alternatively, we can consider that event B has happened, and then consider the probability that A will happen. This is called 'conditional probability' – the probability of A happening conditional on B having happened, and is written The equation for conditional probability is If A and B are independent then so which states the obvious fact that A is independent of B. 