San Francisco State University

• PLSI 551

• Casino Lab Solutions STATION 1. CRAPS c. Probability Questions 1. P(7 or 11) = 6 36 + 2 36 = 8 36 = 2 9 2. P(2, 3, or 12) = 1 36 + 2 36 + 1 36 = 4 36 = 1 9 3. P(roll again) = 1– 2 9 + 1 9 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = 6 9 = 2 3 4. P(win| 8) = 5 11 , since the only outcomes that matter after the first roll are getting an 8 or getting a 7. There are 5 ways to get a sum of 8 and 6 ways to get a sum of 7, so the probability of getting an 8 first is 5/11. d. The probabilities on the branches of the tree diagram should be the answer to parts (c)1, 2, and 3, respectively. Bonus: (win| (win at craps) (win on 1st roll) (win on subsequent roll) 2 (win with 4) (win with 5) (win with 6) (win with 8) (win with 9) (win with 10) 9 2 33 4 4 5 5 5 9 36 9 36 10 36 11 3 P PP P PPPPPP = + =+ + + + + + = + ⋅+ ⋅ + ⋅ + 5 4 4 3 3 244 0.4929 6 11 36 10 36 9 495 ⋅ + ⋅ + ⋅= = STATION 2. ROULETTE 2. b. c. 20 18 18 1 1 0.053 38 38 38 X ii μ = =− ⋅ + ⋅ = =− ∑x p d. ( )2 2 22 20 18 ( 1 ( 0.053...)) (1– ( 0.053...)) 0.9972 38 38 X iX i σ μ = − ⋅ =−−− ⋅ + − ⋅ = ∑ x p 2 0.9972 0.9986 σ σ X X == = e. 12 1 2 0.053 ( 0.053) .106 μ XX X X + = + =− + − =− μ μ 12 1 2 2 22 0.9972 0.9972 1.9