Question 1: There are 25 people in a room. What is the probability that at least two have the same birthday?
Question 2: Consider a game that consists of rolling a regular die. You pay $10 to play the game and the $10 is not returned. If you roll a 1 or 2, you win nothing. If you roll a 3, 4, or 5, you win $8; if you roll a 6 you win $20. What is your expected value for this game?