Question 4.143

4.143 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 2
Taster 1 1 2 3 4 5
1 0.03 0.02 0.01 0.00 0.00
2 0.02 0.07 0.06 0.02 0.01
3 0.01 0.05 0.25 0.05 0.01
4 0.00 0.02 0.05 0.20 0.02
5 0.00 0.01 0.01 0.02 0.06
  1. Why is this a legitimate assignment of probabilities to outcomes?
  2. What is the probability that the tasters agree when rating a wine?
  3. 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?

4.143

(a) All the probabilities are between 0 and 1 and sum to 1. (b) (c)