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1. A game at the fair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on a yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution. b. If you take one spin, what is your expected value? c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.

1. A game at the fair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on a yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution. b. If you take one spin, what is your expected value? c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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1. A game at the fair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on a yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution. b. If you take one spin, what is your expected value? c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.
Transcribed Image Text:1. A game at the fair involves a wheel with seven sectors. Two of the sectors are pink, two of the sectors are orange, two of the sectors are yellow, and one sector is green. Landing on the green sector will give 3 points, landing on a yellow sector will give 1 point; landing on an orange sector will give 0 points, and landing on a pink sector will give -1 point. Let x = the points you have after one spin a. Construct a probability distribution. b. If you take one spin, what is your expected value? c. What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values.
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