When a coin is tossed the possible outcomes are either a Head $\left( H \right)$ or Tail $\left( T \right)$.
Here, coin is tossed three times then the sample space contains,
$S{\text{ }} = {\text{ }}\left\{ {HHH,{\text{ }}HHT,{\text{ }}HTH,{\text{ }}THH,{\text{ }}TTH,{\text{ }}HTT,{\text{ }}TTT,{\text{ }}THT} \right\}$
And $n\left( S \right){\text{ }} = {\text{ }}8$.
(iii) at least $2$ heads
Suppose $C$ be the event of getting at least $2$ head
So,
Then the probability of the event is
∴P(C) = n(C)/n(S)
= 4/8
= ½
(iv) at most $2$ heads
Suppose $D$ be the event of getting at most $2$ heads
Then the probability of the event is
∴P(D) = n(D)/n(S)
= 7/8