Problem IV - [6 points] Suppose that a pie chart for Problem I is used in the construction of a "wheel of fortune" (a pointer and a rotatable board (wheel) reflecting your pie chart). If the wheel is rotated freely and the pointer, after the wheel comes to rest, points to a letter that is your first initial or your last initial, you win. (a) What is the probability of winning? (b) Find the odds against winning. (Recall your homework and the discussions in the eBook) Problem V - [6 points] Considering the 36 possible ordered pairs of numbers (faces) when a pair of fair, six-sided dice is rolled (as the data set in Example 4.2.7 or in Example 4.2 8 of the eBook that we study), answer the following two questions: 1. Are the Event A, containing outcomes (paired data) with both values being even, and Event B, containing outcomes (paired data) with both values being odd, mutually exclusive events (disjoint events)? Show the outcomes comprising each of the two events first, then briefly support your answer to the question. 2. Are the Events C = {(1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3) } and D = {(5, 1), (5, 2), (5, 3), (5, 4), .(5, 5), (5, 6)} statistically independent? Use the "Multiplication Rule" for testing statistical independence that states: if the probability of the occurrence of the shared outcome(s) between two events is equal to the product (multiplication) of the probabilities of occurrence of the two events, those two events are statistically independent