eventually land in a slot, where each slot has an equal chance of capturing the ball. You can place bets on red or black. If the ball lands on your color, you double your money. If it lands on another color, you lose your money. Each round of the game is independent. Let be your winnings from a $1 bet. Throughout this problem, we treat the cost of the bet as sunk and focus on your gross winnings, which will always be a nonnegative number. For example, your gross winnings from a $1 bet can either be $0 (if you lose) or $2 (if you win). 5.1. What is (2)? 5.2. What is ()?