Here is a game: Flip a coin. On a head the player wins $1. On a tail the player loses $1. Steve discovered that the coin that's being used for the game is slightly biased, with probabilities for heads and tails being 50.5% and 49.5%, respectively. He decided to take advantage. Do not use continuity correction in this question.

Questions: 1. Find the mean and variance for the payoff of one game. 2. Suppose Steve plays the game 100 times, find the probability of him winning money.