Question

Three coins are tossed once. Let $A$ denote the event 'three heads show", $B$ denote the event "two heads and one tail show" $C$ denote the event "three tails show" and $D$ denote the event 'a head shows on the first coin" Which events are
(i) mutually exclusive?
(ii) simple?
(iii) compound?

Answer 1

When three coins are tossed the sample space is given by,
$S=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$
$A=\left\{HHH\right\}$
$B=\{HHT,HTH,THH\}$
$C=\left\{TTT\right\}$
$D=\{HHH,HHT,HTH,HTT\}$
$A\cap B=\varphi$
$A\cap C=\varphi$
$A\cap D=\left\{HHH\right\}\ne \varphi$
$B\cap C=\varphi$
$B\cap D=\{HHT,HTH\}\ne \varphi$
$C\cap D=\varphi$
(i) Event $A$ and $B$; event $A$ and $C$; event $B$ and $C$; and event $C$ and $D$ are all mutually exclusive.
(ii) If an event has only one sample point of a sample space, it is called a simple event.
Thus $A$ and $C$ are simple events.
(iii) If an event has more than one sample point of a sample space it is called a compound event. Thus $B$ and $D$ are compound events