J. In a bag there are 4 blue, 5 gray, and 3 black marisies. You select two marbles out of the bag. Assume that you do not replace the first marble before you pick the second marble. Draw a tree diagram to represent this situation 2 all navig isJump a. What is the probability that you select a blue and gray marble? What is the probability that you select a blue marble on the first draw and a black marble on the second draw? C. What is the probability that you select a blue marble on the first draw given that you select a gray marble on the first? BInA d. What is the probability that you select exactly one red marble or exactly one blue marble? e. What is the probability that you select a gray marble on the first drawer given that you selected a black marble on the second draw? f. What is the probability that you select a gray marble on the first draw given that you selected a gray marble on the first draw?1. Select an adult at random. Define events D: person has earned a college degree and T: person's career is teaching, Rank the following probabilities from smallest to largest. Justify your answer. P(D) P(T) P(DIT) P(TID) Greatest: Smallest Justification: 1. Suppose you roll two fair, six sided dice; one red and one green. a. Are the events "sum is 7" and "green dies shows a 4" independent? Justify your answer. b. Are the events "sum is 7" And "green die shows a 4" mutually exclusive? Justify your answer,5. In a certain month, 88% of automobile drivers filled their vehicle with regular gasoline, 2% purchased midgrade gas and 10% bought premium gas. Of those who bought regular gas, 28% paid with a credit card; of those who bought midgrade gas 34% paid with a credit card and of those who bought premium gas 42% paid with a credit card. Suppose we select a customer at random. a. Find the probability that the customer paid with a credit card. b. Suppose the chosen customer paid with a credit card. What's the probability that the customer bought premium gas? 6. At a large university, the probability that a student takes calculus and is on the dean's list is 0.042. The probability that a student is on the dean's list is 0.21. Find the probability that a student takes calculus, given that he or she is on the dean's list