Problem 5 (10 Points)

You have 1 dollar and you owe the mafia 5 dollars. Being just a probabilist, you decide to make a series of bets with a fair coin. You have the choice between two strategies. Bet 1 dollar each time (the timid strategy). or bet as much as you can but no more than necessary to reach a fortune of 5 dollars ( the bold strategy). Find your probability of staying alive in each strategy.