Question

A coin is tossed then a dice is thrown. Let $A$ be the event ''head turns up on the coin and odd number turns up on the dice'' and $B$ be the event ''tail turns up on the coin and an even number turns up on the dice''. Then $A\cap B^{\prime }$ is
(where $H$ represents head and $T$ represents tail)

• A. $\{H1,H3,H5\}$
• B. $\{T2,T4,T6\}$
• C. $\varphi$
• D. $\{H1,H2,H3,H4,H5,H6,T1,T3,T5\}$

Answer 1

The correct option is A $\{H1,H3,H5\}$

The sample space of the experiment is
$S=\{H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6\}$
$A=\{H1,H3,H5\}$
$B=\{T2,T4,T6\}$
$\Rightarrow B^{\prime }=\{H1,H2,H3,H4,H5,H6,T1,T3,T5\}$
$\Rightarrow A\cap B^{\prime }=\{H1,H3,H5\}$