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4.121 Wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabilities for both tasters' ratings of a randomly chosen wine: Taster 1 1 2 3 4 5 1 0.03 0.02 0.01 0.00 0.00 2 0.02 0.07 0.05 0.02 0.01 Taster 2 3 0.01 0.06 0.25 0.05 0.01 0.00 0.02 0.05 0.20 0.02 5 0.00 0.01 0.01 0.02 0.06 a. Why is this a legitimate assignment of probabilities to outcomes? b. What is the probability that the tasters agree when rating a wine?

4.121 Wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabilities for both tasters' ratings of a randomly chosen wine: Taster 1 1 2 3 4 5 1 0.03 0.02 0.01 0.00 0.00 2 0.02 0.07 0.05 0.02 0.01 Taster 2 3 0.01 0.06 0.25 0.05 0.01 0.00 0.02 0.05 0.20 0.02 5 0.00 0.01 0.01 0.02 0.06 a. Why is this a legitimate assignment of probabilities to outcomes? b. What is the probability that the tasters agree when rating a wine?

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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4.121 Wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabilities for both tasters' ratings of a randomly chosen wine: Taster 1 1 2 3 4 5 1 0.03 0.02 0.01 0.00 0.00 2 0.02 0.07 0.05 0.02 0.01 Taster 2 3 0.01 0.06 0.25 0.05 0.01 0.00 0.02 0.05 0.20 0.02 5 0.00 0.01 0.01 0.02 0.06 a. Why is this a legitimate assignment of probabilities to outcomes? b. What is the probability that the tasters agree when rating a wine? c. What is the probability that Taster 1 rates a wine higher than 3? What is the probability that Taster 2 rates a wine higher than 3? 4.122 Wine tasting. In the setting of the previous exercise, Taster I's rating for a wine is 3. What is the conditional probability that Taster 2's rating is higher than 3?
Transcribed Image Text:4.121 Wine tasters. Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the following probabilities for both tasters' ratings of a randomly chosen wine: Taster 1 1 2 3 4 5 1 0.03 0.02 0.01 0.00 0.00 2 0.02 0.07 0.05 0.02 0.01 Taster 2 3 0.01 0.06 0.25 0.05 0.01 0.00 0.02 0.05 0.20 0.02 5 0.00 0.01 0.01 0.02 0.06 a. Why is this a legitimate assignment of probabilities to outcomes? b. What is the probability that the tasters agree when rating a wine? c. What is the probability that Taster 1 rates a wine higher than 3? What is the probability that Taster 2 rates a wine higher than 3? 4.122 Wine tasting. In the setting of the previous exercise, Taster I's rating for a wine is 3. What is the conditional probability that Taster 2's rating is higher than 3?
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