# 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 die,C : The sum is atleast 7 and multiple of 3.Which pairs of these events are mutually exclusive ?

Given :
A pair of dice is rolled
Therefore the sample space S will be
$\left\{\begin{array}{1 1} (1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\\ (2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\\ (3,1)(3,2)(3,3)(3,4)(3,5)(3,6)\\ (4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\\ (5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\\ (6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\end{array}\right\}$
A : The sum is greater than 8.
$\therefore$ The sum should be either 9,10,11 & 12
$\left\{\begin{array}{1 1}(3,6),(4,5),(5,4),(6,3),(4,6)\\(5,5),(6,4),(5,6),(6,5),(6,6)\end{array}\right\}$
B : 2 occurs on either die
$\left\{\begin{array}{1 1}(1,2),(2,1),(2,2),(2,3),(2,4)\\(2,5),(2,4),(3,2),(4,2),(5,2)(6,2)\end{array}\right\}$
C : The sum is atleast 7 and multiple of 3
$\therefore$ The sum is 9 and 12
$\Rightarrow \{(3,6),(4,5),(5,4),(6,3),(6,6)\}$
Pairs which are mutually exclusive :
$A \cap B =\phi\Rightarrow$ A and B are mutually exclusive.
$B \cap C =\phi\Rightarrow$ B and C are mutually exclusive.
$A \cap C =\phi\Rightarrow$ They are not mutually exclusive.
$\therefore A\cap B$ and $B\cap C$ are mutually exclusive.