Mary and Paul are playing a game of tossing a coin. Mary says to Paul, "We will toss the coin until the first head appears. If the first head appears after an odd number of tosses, I win the game. If the first head appears after an even number of tosses, you win the game." They each put $60 into a cup and when one of them wins a game, he or she removes a dollar from the cup. They continue to do this until the cup is empty. Mathematically speaking, how much money will each person remove from the cup?