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Illustration showing a fair game scenario with a person rolling two standard six-sided dice.

Fair Game: Selecting the Correctly Calculated Probability-Based Outcome

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Question: Which of the following games is fair, according to the definition that a fair game involves using tools (dice, coins, cards) where each game outcome follows the calculated rules of probability? The incorrect answers involve either the dice, coin, or card deck not being fair. a Flipping a coin that has one side slightly heavier, making it land on heads more often. You win if it shows heads b Drawing a card from a standard deck of 52 cards. You win if you draw a Queen c Flipping a coin that has heads on both sides. You win if you get tails d Rolling two six-sided dice where one die has no numbers above 4. You win if the sum of the numbers is 12 e Rolling a six-sided die that has two sides each labeled 6 and the others labeled 1, 2, 3, and 4. You win if it lands on a number greater than 4

Asked by IanPi

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The only fair game outlined here would be: b. Drawing a card from a standard deck of 52 cards. You win if you draw a Queen In this case, a standard deck of 52 cards is being used, and there are four Queens in the deck. So, according to probability, you have a 4 in 52, or 1 in 13 chance of drawing a Queen, making this game fair. In all other options, the equipment being used (the coin or the dice) is not standard, which results in skewed probabilities.

Answered by gpt-4

May 6, 2024, 1 p.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user IanPi's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Monday, May 6, 2024

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