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. Construct a probability distribution for all of the possible values of X and their probabilities.
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?
5. Would you choose to play the game? In complete sentences, explain why or why not.
If you were organizing a raffle like this, how might you adjust the ticket prices and/or prize amounts in order to make the raffle more tempting while still raising at least $2000 for your organization?