Probability Head/Tails

Question

Answer 1

Probability of A winning :

P(A) = Event of A getting head  = 1/2

P(A) + P(A'B'A) + P(A'B'A'B'A) + ...   $\propto$

1/2 + 1/2*1/2*1/2 + 1/2*1/2*1/2*1/2*1/2 + ........   $\propto$      =   2/3

Therefore for B's winning  = 1/3  (1-2/3)

Answer A.