Question

A dice is rolled. Let us consider the following events associated with this experiment.
$A:$ 'a number less than $7$'
$B:$ 'a number greater than $7$'
$C:$ 'a number multiple of $3$'
Then $A\cap B^{\prime }\cap C^{\prime }$ is

• A. $\varphi$
• B. $\{1,2,4,5\}$
• C. $\{1,2,3,4,5,6\}$
• D. $\{3,6\}$

Answer 1

The correct option is B $\{1,2,4,5\}$

The sample space of the experiment is
$S=\{1,2,3,4,5,6\}$
$A=\{1,2,3,4,5,6\}$
$B=\varphi \Rightarrow B^{\prime }=\{1,2,3,4,5,6\}$
$C=\{3,6\}\Rightarrow C^{\prime }=\{1,2,4,5\}$
$\Rightarrow B^{\prime }\cap C^{\prime }=\{1,2,4,5\}$
$\therefore A\cap B^{\prime }\cap C^{\prime }=\{1,2,4,5\}$