# What does exhaustive, non exhaustive and mutually exclusive mean in probability

I am doing some work on probability.

I have done some background reading on the definitions on exhaustive, non exhaustive and mutually exclusive but the definitions that I found do not make any sense to me.

Could someone please define exhaustive, non exhaustive and mutually exclusive and give a simple example of each definition.

Let $X$ be the result of rolling one six-sided die, and define events $E_{\mbox{odd}}$ (the result of the roll is odd) and $E_i$ (the result of the roll is $i$).
The collection of events $\{E_{\mbox{odd}},E_1,E_2,E_4,E_6\}$ is exhaustive. (The result must be odd, $1$, $2$, $4$, or $6$.) The collection $\{E_1,E_2,E_3,E_4\}$ is not exhaustive (the result could be $5$ or $6$), though its events are mutually exclusive. The events in $\{E_{\mbox{odd}},E_2,E_4\}$ are mutually exclusive (no two can occur; also, the events are not exhaustive), and the events in $\mathcal E=\{E_{\mbox{odd}},E_1,E_2,E_3,E_4,E_5,E_6\}$ are not mutually exclusive (though $\mathcal E$ is exhaustive), because both $E_{\mbox{odd}}$ and $E_1$ can occur simultaneously.