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	0.03	0.02	0.01	0.00	0.00
2	0.02	0.09	0.05	0.02	0.00
3	0.01	0.05	0.29	0.05	0.01
4	0.00	0.02	0.05	0.20	0.01
5	0.00	0.00	0.01	0.01	0.05

(a) Why is this a legitimate assignment of probabilities to outcomes?

all probabilities are greater than 0 and they sum to 1 all probabilities are greater than or equal to 0  they sum to 1 all probabilities are greater than or equal to 0 and they sum to 1

(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?

Answer 1

(a)

Correct option:

all probabilities are greater than or equal to 0  they sum to 1.

(b)

The probability that the tasters agree when rating a wine is

(c)

Following table shows the row total and column total:

	Taster 2
Taster 1	1	2	3	4	5	Total
1	0.03	0.02	0.01	0	0	0.06
2	0.02	0.09	0.05	0.02	0	0.18
3	0.01	0.05	0.29	0.05	0.01	0.41
4	0	0.02	0.05	0.2	0.01	0.28
5	0	0	0.01	0.01	0.05	0.07
Total	0.06	0.18	0.41	0.28	0.07	1

So,