Let p be the probability that a coin comes up heads on a single toss. Then 1 - p is the probability that a coin comes up tails on a single toss.

Pr(Heads) = Pr(HT) = p(1 - p).

Pr(Tails) = Pr(TH) = (1 - p)p.

Therefore Pr(Heads) = Pr(Tails).

But Pr(Heads) + Pr(Tails) = 1 since HH and TT are ignored. Therefore .....