Question

A bag contain one red and two black balls and a coin is tossed, if it appears head a ball is selected at random else a die is thrown. Consider the following events:
$A:$ getting a tail followed by selection of a red ball
$B:$ getting a head followed by selection of a black ball
$C:$ getting a head followed by selection of a red ball
$D:$ getting a tail followed by selection of a black ball,
then which of the following statement(s) is/are correct ?

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

Answer 1

Answer: (B), (C), (D)

$A$ and $D$ are impossible events

Let $B_1,B_2$ are black balls and $R_1$ is red ball.
Sample space $S=\{H{B}_1,H{B}_2,H{R}_1,T1,T2,T3,T4,T5,T6\}$
Now,
$A:$ getting a tail followed by selection of a red ball
$\Rightarrow A=\left\{\varphi \right\},$
$B:$ getting a head followed by selection of a black ball
$\Rightarrow B=\{H{B}_1,H{B}_2\},$
$C:$ getting a head followed by selection of a red ball
$\Rightarrow C=\left\{H{R}_1\right\},$
$D:$ getting a tail followed by selection of a black ball
$\Rightarrow D=\left\{\varphi \right\}$