Dice Rolls Two Players Compete Against Each Other by Rolling

question 36

Essay

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.

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Definitions:

Induced

Caused or motivated someone or something to act in a certain way.

Liquidated Damages

are a predetermined form of compensation specified within a contract, payable for a breach of contract, where actual damages are difficult to ascertain.

Unreasonable

Not guided by or based on good sense or logic; excessive or beyond reasonable limits.

Exclusive Personal Services

Contractual agreements where an individual agrees to provide their services exclusively to a single employer or client.