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. Suppos
e you buy one ticket. 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?
The easiest way to do this is to plot the points. I used the pythagorean theorem for this one, too. Add the side lengths to get the perimeter: 5 + 5 + 5 + 3 + √40 = 24.32455532 units or just 24 units.
