Question

Three coins are tossed once. Let $A$ denotes the event ''getting three heads'', $B$ denotes the event ''getting two heads and one tail'', $C$ denotes the event ''getting three tails'' and $D$ denotes the event ''getting a head on the first coin''. Which of the following is/are true?

• A. $(A,B,C,D)$ are simple events.
• B. $(B,D)$ are compound events.
• C. $(A,B,C,D)$ are compound events.
• D. $(A,C)$ are simple events.

Answer 1

Answer: (B), (D)

$(A,C)$ are simple events.

The sample set of the experiment is
$S=\{HHH,HHT,HTH,THH,HTT,THT,TTH,TTT\}$

$A=\left\{HHH\right\}$
$B=\{HHT,THH,HTH\}$
$C=\left\{TTT\right\}$
$D=\{HHH,HHT,HTH,HTT\}$

$\therefore (A,C)$ are simple events and $(B,D)$ are compound events.