At a raffle, 1000 tickets are sold at $5 each. There are 20 prizes of $25, 5 prizes of $100, and 1 grand prize of $2000. Suppose you buy one ticket. Let the random variable X represent your net gain (remember that the net gain should include the cost of the ticket) after playing the game once. 1. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. X (Net Gain) Probability 2. Find the expected value of X, and interpret it in the context of the game. 3. If you play in such a raffle 100 times, what is the expected net gain? 4. What ticket price (rounded to two decimal places) would make it a fair game?