1a) i) Let H represent a coin showing heads and T represent a coin showing tails. Let E be the event that you win.
Then your sample space is S = {HH, HT, TH, TT}, and there is only
one way to win, so the set E contains one element (either HH or TT).
Therefore P(E) = n(E) / n(S) = 1/4.
ii) In this scenario S = {HH, TT} as TH and HT are ignored and E = {HH}. Hence
P(E) = n(E) / n(S) = 1/2.