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wrote...
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2 weeks ago
Dice rolls Two players compete against each other by rolling dice - not the traditional dice, though. One face of Alphonso's die has an 8 and the other five faces are all 2's. Bettina's die has four 3's and two 1's on the six faces.

a. They each roll their die, and the player with the highest score wins. Which player has the advantage?  Explain.
b. If Alphonso wins, Bettina pays him $10. How much should he pay her if she wins in order to make the game fair?
c. They decide to change the rules. They'll each roll, and the winner will collect the number of dollars shown on his or her die. For example, If Alphonso rolls a 2 and Bettina rolls a 3, he'll pay her $3. Create a probability model for the amount Alphonso wins.
d. Find the expected value and standard deviation of Alphonso's winnings at this game.
e. If they play this new game repeatedly which player has the advantage? Explain.
Textbook 

Stats: Modeling the World


Edition: 4th
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2 weeks ago
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a. Total outcomes = 36,  Alphonso wins 16 times = 0.4444,  Bettina wins 20 times = 0.5556
Or P(B) = P(A gets 2 ∩ B gets 3) = × =

b. If fair, E(A) = $10 + x  = 0  or x = -8

So if Alphonso wins, he should pay Bettina $8 to make it a fair game.
c.

d. E(X) = $8 + $2 + (-$3) = $0.22
Standard deviation = = = 4.09
e. Alphonso has the advantage, because his expected value is positive. He expects to win an average of $0.22 for each time they play the game.

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