An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:A: the sum is greater than 8, B: 2 occurs on either dieC: the sum is at least 7 and a multiple of 3.Which pairs of these events are mutually exclusive?

Solution: Event $A:$Event that the sum of two dice is greater than $8$.
$A:\left\{\left(4,5\right),\left(5,4\right),\left(6,3\right),\left(3,6\right),\left(4,6\right),\left(6,4\right),\left(5,5\right),\left(6,5\right),\left(5,6\right),\left(6,6\right)\right\}$
Event $B:$Event that $2$ occurs on either dice.
$B:\left\{\left(2,1\right),\left(2,2\right),\left(2,3\right),\left(2,4\right),\left(2,5\right),\left(2,6\right),\left(1,2\right),\left(3,2\right),\left(4,2\right),\left(5,2\right),\left(6,2\right)\right\}$
Event $C:$Event that the sum is at least $7$ and a multiple of $3$.
$C:\left\{\left(4,5\right),\left(5,4\right),\left(6,3\right),\left(3,6\right),\left(6,6\right)\right\}$
Here, $A\cap C\ne \varphi$, so $A$ and $C$ are not mutually exclusive events.
$A\cap B=\varphi ,$ so $A$ and $B$ are mutually exclusive events.
$B\cap C=\varphi ,$ so $B$ and $C$ are mutually exclusive events.