answer all questions with explanation

4. (12 points, 6+6) Suppose one has $1 now, and wants to win an additional N dollars, where N ~ POiSSOIl()\\). He tosses a fair coin repeatedly; if it comes up heads, he wins one dollar, but if it comes up tails, he loses one dollar. He plays this game until one of two events occurs: either he runs out of money and is bankrupted or he reaches his goal. (1). What is the probability that he will ultimately win? (2). On average, how long will his game last