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