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**Educational Website Content: Probability and Game Theory** --- **Problem 10: Congressional Committee Selection** The composition of the 110th Congress is as follows: 52 Republicans, 48 Democrats, and 3 Independents. A committee on aid to higher education is to be formed with 3 Senators chosen at random to head the committee. Here, we use a multinomial distribution to find the probability that the group consists of: a. All Republicans b. All Democrats c. One Democrat, one Republican, and one Independent **Problem 11: Fairness and Expected Value in Games** A person pays $3 to play a game by rolling a single die once. If a 1 or 2 comes up, the person wins nothing. However, if the player rolls a 3, 4, 5, or 6, he or she wins the difference between the number rolled and $3. Tasks: - Calculate the expectation for this game. - Analyze if the game is fair. --- These exercises explore the concepts of probability distribution and expected value, offering insight into real-world applications such as committee selection and the fairness of games.

**Educational Website Content: Probability and Game Theory** --- **Problem 10: Congressional Committee Selection** The composition of the 110th Congress is as follows: 52 Republicans, 48 Democrats, and 3 Independents. A committee on aid to higher education is to be formed with 3 Senators chosen at random to head the committee. Here, we use a multinomial distribution to find the probability that the group consists of: a. All Republicans b. All Democrats c. One Democrat, one Republican, and one Independent **Problem 11: Fairness and Expected Value in Games** A person pays $3 to play a game by rolling a single die once. If a 1 or 2 comes up, the person wins nothing. However, if the player rolls a 3, 4, 5, or 6, he or she wins the difference between the number rolled and $3. Tasks: - Calculate the expectation for this game. - Analyze if the game is fair. --- These exercises explore the concepts of probability distribution and expected value, offering insight into real-world applications such as committee selection and the fairness of games.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Website Content: Probability and Game Theory** --- **Problem 10: Congressional Committee Selection** The composition of the 110th Congress is as follows: 52 Republicans, 48 Democrats, and 3 Independents. A committee on aid to higher education is to be formed with 3 Senators chosen at random to head the committee. Here, we use a multinomial distribution to find the probability that the group consists of: a. All Republicans b. All Democrats c. One Democrat, one Republican, and one Independent **Problem 11: Fairness and Expected Value in Games** A person pays $3 to play a game by rolling a single die once. If a 1 or 2 comes up, the person wins nothing. However, if the player rolls a 3, 4, 5, or 6, he or she wins the difference between the number rolled and $3. Tasks: - Calculate the expectation for this game. - Analyze if the game is fair. --- These exercises explore the concepts of probability distribution and expected value, offering insight into real-world applications such as committee selection and the fairness of games.
Transcribed Image Text:**Educational Website Content: Probability and Game Theory** --- **Problem 10: Congressional Committee Selection** The composition of the 110th Congress is as follows: 52 Republicans, 48 Democrats, and 3 Independents. A committee on aid to higher education is to be formed with 3 Senators chosen at random to head the committee. Here, we use a multinomial distribution to find the probability that the group consists of: a. All Republicans b. All Democrats c. One Democrat, one Republican, and one Independent **Problem 11: Fairness and Expected Value in Games** A person pays $3 to play a game by rolling a single die once. If a 1 or 2 comes up, the person wins nothing. However, if the player rolls a 3, 4, 5, or 6, he or she wins the difference between the number rolled and $3. Tasks: - Calculate the expectation for this game. - Analyze if the game is fair. --- These exercises explore the concepts of probability distribution and expected value, offering insight into real-world applications such as committee selection and the fairness of games.
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