A game of chance is described. a. Is the game fair? b. If...

A game of chance is described. a. Is the game fair? b. If the game is not fair, find the payout amount that would make the game fair.
A die is rolled. You get $\$ 20$ if a one or a six shows; otherwise, you pay $\$ 10$..

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Key Concepts

Probability

Probability is the measure of the likelihood that an event will occur. In games of chance, calculating the probability of various outcomes is essential for understanding the risks and rewards associated with each potential outcome.

Expected Value

Expected value is a key concept in probability and statistics, representing the average result of a random event when repeated many times. It is calculated by multiplying each outcome by its probability and summing these products. This concept is crucial for determining whether a game is advantageous, neutral, or disadvantageous over the long run.

Game Fairness

A game is deemed fair when the expected value is zero, meaning that the average gain or loss over many iterations of the game is zero. Determining fairness involves comparing the probabilities and payouts of different outcomes to ensure that they balance out.

Payout Calculation

Payout calculation involves adjusting the rewards or penalties associated with different outcomes to achieve a desired expected value, often zero for a fair game. This process typically requires setting up an equation that balances the overall expected returns from the game.

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