Hello, I need 3,5,6,7, and 8. 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).

1. Use the table below to help you construct a probability distribution for all of the possible values of Xand theirprobabilities.

(Net Gain)	Probability
7992	1/2500=0.0004
492	10/2500=0.004
92	30/2500=0.012
-8	2459/2500=0.9836

2. Find the mean/expected value of X. (Round to two decimalplaces.)

Answer: $-1.6

3. In complete sentences, describe the interpretation of what your value from #2 represents in the context of theraffle.

Answer: -1.6 represents the amount of money you will lose if you decide to buy one ticket.

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

Answer: If I were to play in such a raffle, the expected net gain would be $-160.

5. 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.)

Answer:

6. 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 decimalplaces.)

Answer:

7. 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 atleast$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.

Answer:

8. Construct a new probability distribution describing the net gain (fromthe player's perspective) for the game with your proposed changes from#7.

Answer: