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?

Have you ever been in the middle of telling a story and had to use hand gestures or even a drawing to make your point? in algebra, if we want to illustrate or visualize a key feature of a function, sometimes we have to write the function in a different form—such as a table, graph, or equation—to determine the specific key feature we’re looking for. think about interactions with others and situations you’ve come across in your own life. how have you had to adjust or change the way you represented something based on either the concept you were trying to describe or the person you were interacting with? explain how the complexity or layout of the concept required you to change your style or presentation, or how the person’s unique learning style affected the way you presented the information.