An experiment consists of tossing 3 coins ∴ The sample space of the given experiment is given by S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} ∴ n(S) = 8 (i) Let E be the event that 3 heads appear ∴ n(E) = 1 (Since E = {HHH}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{1}{8}$ (ii) Let E be the event that 2 heads appear ∴ n(E) = 3 (Since E = {HHT, HTH, THH}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{3}{8}$ (iii) Let E be the event that atleast 2 heads appear ∴ n(E) = 4 (Since E = {HTH, HHT, THH, HHH}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{4}{8}$ = $\frac{1}{2}$ (iv) Let E be the event that at most 2 heads appear ∴ n(E) = 7 [Since E = HHT, HTH, THH, TTT, THT, TTH, HTT] ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{7}{8}$ (v) Let E be the event that no head appears ∴ n(E) = 1 (Since E = {TTT}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{1}{8}$ (vi) Let E be the event that 3 tails appear ∴ n(E) = 1 (Since E = {TTT}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{1}{8}$ (vii) Let E be the event that exactly two tails appear ∴ n(E) = 3 (Since E = {TTH, THT, HTT}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{3}{8}$ (viii) Let E be the event that no tail appears ∴ n(E) = 1 (Since E = {HHH}) (ix) Let E be the event that atmost two tails appear ∴ n(E) = 7 (Since E = {THH, HTH, HHT, HTT, THT, TTH, HHH}) ⇒ P (E) = $\frac{n(E)}{n(S)}$ = $\frac{7}{8}$