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# Three coins are tossed,describe : Three events which are mutually exclusive but not exhaustive.

Three coins are tossed.
$\therefore$ The sample space =$2^3=8$ possible outcome
$S=\{HHH,HHT,HTH,HTT,THH,THT,TTH,TTT\}$
Let A be the event "Exactly one tail"
$A=\{HTH,HHT,THH\}$
Let B be the event "Exactly two tail"
$B=\{HTT,THT,TTH\}$
Let C be the event "Exactly three tails"
$\therefore C=\{TTT\}$
$\therefore A\cap B \cap C=\phi$ but $A\cup B \cup C\neq S$
$\therefore A,B$ and C are mutually exclusive but not exhaustive.