Question

In an experiment a coin is tossed; if in first trials, it appears head then the coin is tossed again else a die is rolled. consider the following events:
$A:$ getting two heads
$B:$ getting two tails
$C:$ getting head followed by ${}^{\prime }{6}^{\prime }$ on the die
$D:$ getting tail followed by ${}^{\prime }{1}^{\prime }$ on the die

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

Answer 1

Answer: (B), (C)

$A$ and $D$ are simple events

From given experiment:
sample space $S=\{HH,HT,T1,T2,T3,T4,T5,T6\}$
According to statement :
As,$A:$ getting two heads
$\Rightarrow A=\left\{HH\right\},$
$B:$ getting two tails
$\Rightarrow B=\left\{\varphi \right\},$
$C:$ getting head followed by ${}^{\prime }{6}^{\prime }$ on the die
$\Rightarrow C=\left\{\varphi \right\},$
$D:$ getting tail followed by ${}^{\prime }{1}^{\prime }$ on the die
$\Rightarrow D=\left\{T1\right\}$