(i) When one coin is tossed twice, the sample space is 

S = {HH,HT,TH,TT}. 

Let X denotes, the number of heads in any outcome in S, 

X (HH) = 2, X (HT) = 1, X (TH) = 1 and X (TT) = 0 

Therefore, X can take the value of 0, 1 or 2. It is known that 

P(HH) = P(HT) = P(TH) = P(TT) = 1/4 

∴ P(X = 0) = P (tail occurs on both tosses) = P({TT}) = 1/4 

P(X = 1) = P (one head and one tail occurs) = P({TH,HT}) = 2/4 = 1/2 

and P(X = 2) = P (head occurs on both tosses) = P({HH}) = 1/4 

Thus, the required probability distribution is as follows

(ii) When three coins are tossed thrice, the sample space is 

S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} which contains eight equally likely sample points. 

Let X represent the number of tails. Then, X can take values 0, 1, 2 and 3. P(X = 0) = P (no tail) = P({HHH}) = 1/8 , P (X = 1) = 

P (one tail and two heads show up) = P({HHT,HTH,THH}) = 3/8,

P (X = 2) = P (two tails and one head show up) = P({HTT,THT,TTH}) = 3/8 

and P(X = 3) = P (three tails show up) = P({TTT}) = 1/8 

Thus, the probability distribution is as follows