4.133 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 |
(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?