Question

2. (25 points) Sekora International Casino (SIC) is launching a new game making use of fair 6-sided dice . In phase 1, roll two 6-sided dice and compute the difference between the rolls. Call this difference . In phase 2, roll r dice, and add up the total of the rolls. This is the payout in dollars of the game. (with the numbers 1-6 on the sides). The game proceeds in two phases as follows: (a) (5 points) In the first phase of the game,エcan take on any value 0-5. Compute the probability as a fraction) for each of these outcomes to fill in the following table. valT0一ㄧ一ㄒㄧ一 --T4-ㄧㄧㄧㄧㄒ 5 12 1-3 P(z=val)! (b) (5 points) For each value of r, what is the average payout (expected value) of the game? expected value (c) (5 points) If Sekora International Casino wants to make an average of $1 in profit per play, how much should they charge per play? (Hint: Use your answers to the previous two parts.) (d) (10 points) Professor Kruskal tells you that he won $4 in one play of the game. Given this infor- mation, what is the probability that he had 1 in the first phase of the game?

Answer 1

2nol 1/ 6 5 i- 1 I S 4. 3t 2.

頭 1 8 io. 2 3-5 2 xpected voluEX) 10.5 emyected vabun Ex) 14. 거 5 3 16

PC total rag Duet= $1) PCI, IL + 十P(1) 2 2 16 3 13