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Expected Value, Cost, Expected Profit

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A game company that manufactures a dart game that dispenses tickets has been asked to put a business plan together for a customer who wishes to buy the game. The dart game gives 5 tickets for a score of 50, 4 tickets for a score of 40, 3 tickets for a score of 30, two tickets for a score of 20, 1 ticket for a score of 10, and no tickets if the board is not hit.

The probabilities of getting each score are as follows:

Score Probability
50 1/32
40 1/16
30 1/8
20 1/4
10 1/2
0 1/32

The customer will be exchanging the tickets for stuffed animals that cost $3.00 each. Prepare a report for the customer that presents the expected value in points of each throw of the darts, and then present a graphic representation of a at least three plans relating cost per dart, cost in tickets of the animals, and expected profit. Include a one or two paragraph summary of the possible plans.

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