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:

States

In the context of the United States, states are the constituent political entities that share sovereignty with the federal government and have their own government and constitution.

Equitable Remedy

A form of justice administered according to fairness as contrasted with strictly formulated rules of common law.

Specific Performance

A legal remedy in contract disputes where a court orders the party who breached the contract to fulfill their obligations as specifically stated in the contract, rather than just paying damages.

Promised Act

An action that a party commits to carrying out, often referenced in the context of contractual agreements.