Question

Let there are $10$ cards of numbered $1$ to $10,$ one card is selected at random. Consider the following events:
$A:$ The number on selected card is divisible by $2$
$B:$ The number on selected card is odd.
If $S$ is the sample space, then which of the following is/are correct ?

• A. $A\cup B=S$
• B. $A\cup B=A$
• C. $A\cap B=B$
• D. $A\cap B=\varphi$

Answer 1

Answer: (A), (D)

$A\cap B=\varphi$

sample space $S=\{1,2,3,4,5,6,7,8,9,10\}$
$A=\{2,4,6,8,10\}$
$B=\{1,3,5,7,9\}$
$\Rightarrow A\cup B=\{1,2,3,4,5,6,7,8,9,10\}=S$
$\Rightarrow A\cap B=\varphi$