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# Three coins are tossed,describe two events which are not mutually exclusive

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 "At most two tails"
$\therefore A=\{HHH,HHT,HTH,HTT,THH,THT,TTH\}$
Let B be the event "Exactly two tails"
$\therefore B=\{HTT,THT,TTH\}$
$\therefore A\cap B=\{HTT,THT,TTH\}\neq \phi$
$\therefore$ A and B are not mutually exclusive.
edited Jun 27, 2014