Suppose that a balanced die is rolled repeatedly until the same number appears on two successive rolls, and let X denote the number of rolls that are required. Determine the value of Pr(X = x), for x = 2, 3, . . . . 23. Suppose that 80 percent of all statisticians are shy, whereas only 15 percent of all economists are shy. Suppose also that 90 percent of the people at a large gathering are economists and the other 10 percent are statisticians. If you meet a shy person at random at the gathering, what is the probability that the person is a statistician?