Question

Let there are $8$ cards numbered $1$ to $8,$ even numbered card is red coloured and odd numbered card is black coloured.
A card is selected at random,
Consider the following events:
$A:$ The selected card is red and the number on the card is divisible by $5.$
$B:$ The selected card is black and the number on the card is divisible by $7$
$C:$ The selected card is red and the number on the card is divisible by $4$
$D:$ The selected card is black and the number on the card is divisible by $3.$
Then which of the following statement(s) is are correct ?

• A. $A$ is impossible event.
• B. $B$ and $C$ are simple events.
• C. $B$ and $D$ are simple events.
• D. $C$ is compound event.

Answer 1

Answer: (A), (C), (D)

$C$ is compound event.

Given : sample space $S=\{2R,4R,6R,8R,1B,3B,5B,7B\}$
Here, $R-$Red, $B-$Black
According to question,
$A=\left\{\varphi \right\},$ (As, odd numbered card is black)
$B=\left\{7B\right\},$
$C=\{4R,8R\}$
$D=\left\{3B\right\}$
We know, simple event have only one sample point in sample space.
and compound event consists more than one sample point.