Browse Questions

# Two dice are thrown.The events A,B and C are as follows :A : getting an even number in first die,B : getting an odd number on the first die,C : getting the sum of the numbers on the dice $\leq$ 5.State true or false : A',B' and C are mutually exclusive & exhaustive

$\begin{array}{1 1}(A)\;\text{True}\\(B)\;\text{False}\end{array}$

Given two dice are thrown
Possible outcomes =$6\times 6=36$
$\therefore$ The sample space
$S=\left\{\begin{array}{1 1}(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)\\(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)\\(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)\\(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)\\(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)\\(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)\end{array}\right\}$
A: Getting an even number on first die
A': Getting an odd number on first die
B': Getting an even number on first die
C:Getting the sum of the numbers on the dice $\leq 5$
$A' \cap B'=\phi$
But $A'\cup B' \cap C=S$
$A'\cap C=B\cap C=\{(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)\}\neq \phi$
$B'\cap C=A\cap C=\{(2,1),(2,2),(2,3),(4,1\}\neq \phi$
$\therefore A',B'$ and $C$ are not mutually exclusive but exhaustive.
Hence the given statement is False.