These questions pertain to textbook (Introduction to Probability) Example 1.20 where Peter and Mary take turns rolling a fair die. To answer the questions, be precise about the definitions of your events and their probabilities. (a) As in Example 1.20, suppose Peter takes the first roll. What is the probability that Mary wins and her last roll is a six? (b) Suppose Mary takes the first roll. What is the probability that Mary wins? (c) What is the probability that the game lasts an even number of rolls? Consider separately the case where Peter takes the first roll and the case where Mary takes the first roll. Based on your intuition, which case should be likelier to end in an even number of rolls? Does the calculation confirm your intuition?