Please help me with this.

4. Gambler's ruin . Fix a probability p E [0, 1:]. Play a sequence of games; in each game you (independently) win $1 with probability p and lose $1 with probability q and you make nothing with probability 1 p :3. Assume that your initial capital is i dollars and that you play until you either reach a predetermined amount N, or you lose all your money. You are interested in the probability P;- that you leave the game happy with your desired amount N. (a) Compute is p0,pN, the probability that you win the game with 0 initial capital and win the game starting with N initial capital. (b) Write the recurrence relationship which expresses p" in terms of pn_;,pn+1 (c) Find the probability of winning when N=10|3, and p = .5,q = .4 and initial money i = 30