2. (a) Suppose the sophomore class at BU is surveyed on their choices of majors: From the menu {Economics, Math, Computer Science}, 33% choose economics, 27% choose math, and 40% choose Computer Science. From the menu {Math, Computer Science}, 20% choose math and 80% choose computer science. From the menu {Economics, Math, English, History, Neuroscience} 27% choose eco- nomics, 15% choose math, 7% choose English, 25% choose history, and 26% choose neuroscience. Do these choices satisfy regularity? (b) Suppose instead the sophomore class at BC is surveyed on their choices of majors from different menus: From the menu {Economics, Math, Computer Science}, 72% choose economics, 18% choose math, and 10% choose Computer Science. From the menu {Economics, Math, English}, 30% choose economics, 54% choose math, and 16% choose English. 1 These choices do not formally violate regularity, because neither of the menus and {Economics, Math, Computer Science} {Economics, Math, English} are contained in the other. Suppose the BC sophomores were also asked about the menu {Economics, Math}. Are there probabilities PE and PM of choosing math and economics such that their choices would satisfy the regularity condition? Give probabilities that satisfy regularity or explain why there are none.