At a raffle, 1000 tickets are sold for $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.
2. Find the mean (expected value) of your net gain X, and interpret what this value means in the context of the game.
3. If you play in such a raffle 100 times, what is the expected value of your
net gain? (Hint: Use your answer from #2.)
4. What ticket price would make it a fair game? (The game is “fair” if the money is balanced so that neither side, the players or the organizers of the raffle, wins/loses money on average. )
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 price and/or prize amounts in order to make the raffle more tempting while still raising at least $2000 for your organization?
