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.