At a raffle, 1000 tickets are sold for exist5 each. There are 20 prizes of exist

Question

At a raffle, 1000 tickets are sold for exist5 each. There are 20 prizes of exist25, 5 prizes of exist100, and 1 grand prize of exist2000. 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. Use the table below to help you construct a probability distribution for all of the possible values of X and their probabilities. Find the mean (expected value) of your net gain X, and interpret what this value means in the context of the game. If you play in such a raffle 100 times, what is the expected value of your net gain? 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.) Would you choose to play the game? In complete sentences, explain why or why not. 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 exist2000 for your organization?

Explanation / Answer

1)

2) Expected value of net gain = 20x20/1000 + 95x5/1000 + 1995x1/1000 - 5x974/1000

= -2 dollars

So, there is a loss of $2 expected

3) if such raffle is played 100 times, expected outcome = -2x100 = -200 dollars

That is, a loss of $200

4) to make it a fair game, ticket price must be 5 - 2 = $3 each

5) Giving 10 prices of $25, 5 prices of $50 and 1 mega prize of $5000 will attract more people. For this if the ticket prize is set as $8, the amount that can be raised is $2500

X (net gain) Probability 20 20/1000 = 1/50 95 5/1000 = 1/200 1995 1/1000 -5 974/1000

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