1. (2 pts) An experiment consists of drawing cards from a standard 52-card deck without replace- ment. Let X = the number of cards drawn until all four Queens are drawn. List the possible values of X and classify the random variable. (NOTE: choose one answer from each column) (a) X = {1, 2, 3, . . ., 49} (b) X - {4, 5, 6, . . ., 52} (a) finite discrete (c) X = {5, 6, 7, . .., 52} (b) infinite discrete (d) X = {1, 2, 3, . . .} (e) X = {4, 5, 6, ...} (c) continuous (f) X E [1, 52] 2. (2 pts each) Determine in each case if A and B are independent, mutually exclusive, or neither. (a) P(A) = 0.4, P(B) = 0.5, P(A UB) = 0.7 (b) P(A) = 0.3, P(B) = 0.6, P(A U B) = 0.93. (4 pts) An optometry patient is tested for glaucoma. The test falsely detects glaucoma in 5% of patients who do not have it. The test also fails to detect glaucoma in 3% of patients who do have it. If 15% of the US population has glaucoma, what is the probability that a person who tests positive for glaucoma actually has it