<P> where S is the sample space . </P> <P> Compare this to the concept of a set of mutually exclusive events . In such a set no more than one event can occur at a given time . (In some forms of mutual exclusion only one event can ever occur .) The set of all possible die rolls is both collectively exhaustive and mutually exclusive . The outcomes 1 and 6 are mutually exclusive but not collectively exhaustive . The outcomes "even" (2, 4 or 6) and "not - 6" (1, 2, 3, 4, or 5) are collectively exhaustive but not mutually exclusive . In some forms of mutual exclusion only one event can ever occur, whether collectively exhaustive or not . For example, tossing a particular biscuit for a group of several dogs cannot be repeated, no matter which dog snaps it up . </P> <P> One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin . The outcome must be either heads or tails, or p (heads or tails) = 1, so the outcomes are collectively exhaustive . When heads occurs, tails can't occur, or p (heads and tails) = 0, so the outcomes are also mutually exclusive . </P> <P> The term "exhaustive" has been used in the literature since at least 1914 . Here are a few examples: </P>

If events a and b are mutually exclusive are they also collectively exhaustive