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.

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?

5.            Would you choose to play the game?  In complete sentences, explain why or why not.

6.            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?