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# 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 toss" which events are mutually exclusive ?

Toolbox:
• To know whether an event is mutually exclusive $A\cap B =\phi$
Given three coins are tossed.
Therefore,the sample space (ie) $2^3=8$ possible outcome
$S=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$
Given :
B=Two heads and one tail show ={HHT,HTH,THH}
C=Three tail show ={TTT}
D=A head shows on the first toss={HHH,HHT,HTH,HTT}
Here $A \cap B=\phi$
$A \cap C=\phi$
$A \cap D\neq \phi$
$B \cap C= \phi$
$B \cap D\neq \phi$
$C \cap D= \phi$
$A \cap B \cap C= \phi$
It is clear that A and B ,A and C,B and C,C and D and A,B and C are mutually exclusive.