Alex is given a choice between two games. In Game 1, a fair coin is flipped and if it comes up heads, Alex receives $100. If the coin comes up tails, Alex receives nothing. In In-game 2, a fair coin is flipped twice. Each time the coin comes up heads, Alex receives $50, and Alex receives nothing for each coin flip that comes up tails. Assuming that Alex has a monotonically increasing utility function for money in the range [$0, $100], show mathematically that if Alex prefers Game 2 to Game 1, then Alex is risk-averse (at least with respect to this range of monetary amounts).