A charity organization hosts a raffle drawing at a fund-raising event. The organization sells 2500 tickets at a price of $8 each. Winning tickets are randomly selected, with 30 prizes of $100, 10 prizes of $500, and 1 grand prize of $8000.

- Suppose you buy one ticket. Let the random variable Xrepresent your net gain from playing the game once (remember that the net gain should include the cost of the ticket).

- Find the mean/expected value of . Round to at least two decimal places.

-If you were to play in such a raffle 100 times, what is the expected net gain?

- Would you choose to buy a ticket for the raffle? (Your response should be a short paragraph, written in complete sentences, to explain why or why not.)

- What ticket price would make it a fair game, so that, on average, neither the players nor the organizers of the raffle win or lose money? (Round to two decimal places.)

If you were organizing a raffle like this, how would you change the game (ticket prices, number of tickets, prize amounts, etc.) in order to encourage more people to purchase tickets while still raising at least $4000 for your organization? Your response should include a short paragraph, written in complete sentences, with an explanation of the specific adjustments or changes that you would make and how these changes would encourage more people to purchase tickets.

- Construct a new probability distribution describing the net gain (fromthe player's perspective)