ISI sample 2015 - Maths

[Rajat]

Puja and Priya play a fair game (i.e. winning probability is ½ for both players)
repeatedly for one rupee per game. If originally Puja has a rupees and Priya
has b rupees (where a>b), what is Puja’s chances of winning all of Priya’s money,
assuming the play goes on until one person has lost all her money?
(a) 1 (b) 0 (c) b/(a+b) (d) a/(a+b)

[L]

This is the famous Gambler's Ruin problem. Answer: a/(a+b)