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 mutually exclusive?

(N/A) When three coins are tossed,the sample space is given by
$S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$
Accordingly,
$A = \{HHH\}$
$B = \{HHT, HTH, THH\}$
$C = \{TTT\}$
$D = \{HHH, HHT, HTH, HTT\}$
Two events are mutually exclusive if their intersection is the empty set $(\phi)$.
$A \cap B = \phi$
$A \cap C = \phi$
$A \cap D = \{HHH\} \neq \phi$
$B \cap C = \phi$
$B \cap D = \{HHT, HTH\} \neq \phi$
$C \cap D = \phi$
Thus,the mutually exclusive pairs are $(A, B)$,$(A, C)$,$(B, C)$,and $(C, D)$.