tossing a coin

i) if the outcome is T, it does not give the outcome, so ignore this
when the outcome is H, then there is two possibilities
one is H and one is T
the probability of getting a H now is 1/2, and if it is not H then it gives a T
so the probability of the pattern HH before the pattern HT is 1/2

ii) if the outcome is T first, its probability is 1/2
once there is a T, then it will give TH eventually, the pattern may be TT..TTH
so the only chance that the pattern HH before the pattern TH is
to get HH at the first two toss (since once there is a T, it will give TH pattern)
so the probability is 1/2 x 1/2 = 1/4