## When three coins are tossed once the sample space is given by

$S=HHH,HHT,HTH,THH,HTT,THT,TTH,TTT$

$∴$ Accordingly $n(S)=8$

It is known that the probability of an event $A$ is given by

$P(A)=$ $TotalnumberofpossibleoutcomesNumberofoutcomesfavourabletoA =n(S)n(A) $

(i) Let $B$ be the event of the occurrence of $3$ heads Accordingly $B=HHH$

$∴P(B)=n(S)n(B) =81 $

(ii) Let $C$ be the event of the occurrence of $2$ heads Accordingly $C=HHT,HTH,THH$

$∴P(C)=n(S)n(C) =83 $

(iii) Let $D$ be the event of the occurrence of at least $2$ heads

Accordingly $D=HHH,HHT,HTH,THH$

$∴P(D)=n(S)n(D) =84 =21 $

(iv) Let $E$ be the event of the occurrence of at most $2$ heads

Accordingly $E=HHT,HTH,THH,HTT,THT,TTH,TTT$

$∴P(E)=n(S)n(E) =87 $

(v) Let $F$ be the event of the occurrence of no head

Accordingly $F=TTT$

$∴P(F)=n(S)n(F) =81 $

(vi) Let $G$ be the event of the occurrence of $3$ tails

Accordingly $G=TTT$

$∴P(G)=n(S)n(G) =81 $

(vii) Let $H$ be the event of the occurrence of exactly $2$ tails

Accordingly $H=HTT,THT,TTH$

$∴P(H)=n(S)n(H) =83 $

(viii) Let $I$ be the event of the occurrence of no tail

Accordingly $I=HHH$

$∴P(I)=n(S)n(I) =81 $

(ix) Let $J$ be the event of the occurrence of at most $2$ tails

Accordingly $I=HHH,HHT,HTH,THH,HTT,THT,TTH$

$∴P(J)=n(S)n(J) =87 $