(1) A air die is rolled and the sample space is given as S = {l,2,3,4,5,5}. Let A = {1,2} and B = {3, 4}. 1Which of the following statements is true? A. A and B are disjoint. B. P(A U B) = 4,16. 0. PU; U B) = PM.) + PUB). D. All of the answer options are correct. (2) Horses are housedin pastures, pipe pens, or barnstalls at a local horse barn. A = {horses housed in barn stall} and B 2 {horses not housed in barn stall}. Which statement is true? A. B is the complement to A. B. A and B are disjoint. C. P(A U B) = PM.) + PUB). D. All of the answer options are correct. (3) For a particular surgery, infection occurs in 3% of such operations, the repair fails in 14%, and both infection and failure occur together in 1%. What percent of these operations succeed and are free from infection? A. 3% - 14% B. 3% -- 14% - 1% C. 1 - {3% +14% - 1%) D. 1 - {3% + 14%) (4) Assume that you are about to buy a car. There is a probability of 0.4 that you will purchase a new vehicle, and a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will go home with more than one vehicle. Which of the following is true? A. The probability that you will not buy a used vehicle is 0.5. B. If you buy a new car, then you will not buy a used car. C. Purchasing a new car and purchasing a used car are disjoint events. D. All of the answer options are correct. {5) Assume that you are about to buy a car. There is a probability of 0.4 that you will purchase a new vehicle, and a probability of 0.5 that you will purchase a used vehicle. There is no probability that you will go home with more than one vehicle. The probability that you purchase no vehicle at all is: A. 0 B. 0.1 C. 0.9 D. 1