"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 2Taster 11234510.030.020.010.000.00"

2 0.02 0.07 0.06 0.02 0.01 W 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? 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