Question

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	0.04	0.03	0.02	0.00	0.00
2	0.03	0.09	0.05	0.02	0.00
3	0.02	0.05	0.20	0.05	0.02
4	0.00	0.02	0.05	0.20	0.02
5	0.00	0.00	0.02	0.02	0.05

a. What is the probability that the tasters agree when rating a wine?

b. What is the probability that Taster 1 rates a wine higher than 3?

c. What is the probability that Taster 2 rates a wine higher than 3?

Answer 1

	Taster 2
Taster 1	1	2	3	4	5	total
1	0.04	0.03	0.02	0	0	0.09
2	0.03	0.09	0.05	0.02	0	0.19
3	0.02	0.05	0.2	0.05	0.02	0.34
4	0	0.02	0.05	0.2	0.02	0.29
5	0	0	0.02	0.02	0.05	0.09
total	0.09	0.19	0.34	0.29	0.09	1

a)

probability that the tasters agree when rating a wine =P(X=1,Y=1)+P(X=2,Y=2)+P(X=3,Y=3)+P(X=4,Y=4)+P(X=5,Y=5)=0.58

b)

probability that Taster 1 rates a wine higher than 3 =0.29+0.09=0.38

c)

probability that Taster 2 rates a wine higher than 3 =0.29+0.09=0.38