Question 5. (10 points) A carnival has a dart game consisting of three circles with different payoffs as: (Nothing is won if the player misses the dart board) B$5 Over time the operator has learned that when a customer throws a dart, they hit each region with the fol- lowing probabilities: p(A) - 0.02. p(B) - 0.06, and p(C) - 0.1. a) What is the expected payoff for one throw of a dart? b) If a customer pays $5 to throw 3 darts, how much can the carnival expect to make per customer? (If a customer throws all three darts in A they win $20 + S20+$20 - $60, etc....) Question 6. (8 points) Let S be the set of all people. Test the following binary relations on S for reflex- ivity, symmetry, antisymmetry, and transitivity. a) x is taller than y b) x and y were born on the same day c) x has the same first name as y d) x and y have a common biological grandparent Revision 5/2017