Question: 1. Sixteen dice are rolled, and unordered results are recorded. If at least five sixes come up, the player wins $70, otherwise the player pays $4. What is the player's expected value?
2. Seven hats are in a closet. Four are black and three are red. A person reaches in and pulls out four hats, without regard to order. If at least two are red, the player wins $10. Otherwise the player loses $5. What is the player's expected value?
3. Six coins are flipped, then four dice are rolled. If four heads or a total of at least 24 on the dice result, the player wins $25. Otherwise the player loses $3. What is the expected value of this game?