1. Suppose you design a game with outcomes A, B and C for which you can estimate probabilities Pr(A) = 0.01, Pr(B) = 0.09 and Pr(C) = 0.9. It costs the player $1 to play each time. If outcome C occurs, they win nothing. If outcome A occurs, they win $50. They will also win some money if B occurs. What is the largest amount paid out for B in whole dollars which will make the game break even or make a pro?t for you on average? Show working to justify your answer.
2. In all of the following questions 7 coupons are being distributed into 4 showbags. In each case determine the number of ways it can be done, showing working.
(c) Suppose that there are 4 different types of show bag and the coupons are identical and the bags are non-empty.
(d) Suppose the coupons and bags are both distinct but the bags are allowed to be empty.
Need some help for these tutorial questions!