Rolling two fair dice At the Spring Bazaar Charity Fundraiser, you play a game in which you roll two dice. (All proceeds go to the charity.) The game costs $1 to play. If you roll a sum of 2, you win $4. If you roll a sum greater than 2 and at most 4, you win $1. If you roll a sum of 11, you win $0.50. If you roll a sum of 12, you must donate an additional $1 to the charity. If you roll any other sum, the game is over. Complete the table to find the expected value of this game from the point of view of the Spring Bazaar Fundraising committee. Round all dollar values to two decimal places. Event Value Probability Value x Probability sum of 2 $   $ 2

Avi and Benita are playing a game. They both start at 100 points (round 0). • At the end of each round, Avi earns 500 points. • At the end of each round, Benita's points double. At the start of what round will Benita take the lead? By how many points? Round 6, 600 points Round 6, 500 points Round 5, 500 points Round 5, 600 points

Cycling Race Three friends, Xavier, Yolanda, and Zeke, want to have a race on their stationary bikes. Aware that he is the fastest rider, Xavier claims he can ride n3 miles faster than Yolanda can ride n miles and Zeke can ride log3 n miles, for any value of n. Suppose Xavier's speed is 60 miles per hour, Yolanda's speed is 20 miles per hour, and Zeke's speed is 3 miles per hour. We will show that Xavier is incorrect (he has never taken a Discrete Structures course, evi- dently!). (a) How large must n be to ensure that Yolanda finishes before Xavier? Justify the answer. (b)How large must n be to ensure that Zeke finishes before Xavier? Justify the answer. (c) As n gets increasingly large, who completes their ride first, Zeke or Yolanda? Justify The answer. Answer: