Jenny decided to enjoy her weekend in Las Vegas with $ x, and each time she bets, she either win $ 1 with probability p or lose $ 1 with probability 1 - p. Denote {Xn} as her wealth after nth bet.

a) Let 0 be the first time her wealth reaches 0 (she gets bankrupt), and let c be the first time her wealth reaches c (she feels she wins enough money to stop). Please verify that for p does not equal to 1/2, P(c < 0) = (1-(q/p)^a)/(1-(q/p)^c) (you also need to consider the case she starts with $ c or $ 0)

b). Instead of winning $1 or losing $1, Jenny has 1/4 probability to win $1, 1/4 probability to win/lose nothing and 1/2 probability to lose $1. Compute (0 < infinity).

I already figured out question a. Could you help me with question b here? Hope you could provide me with full steps and explanations.