2. You are sitting on Go in a Monopoly game. Assume that you roll two fair indep

Question

2. You are sitting on Go in a Monopoly game. Assume that you roll two fair independently. Before you roll, you see the following potential results (amount of money you will win (positive) or lose (negative)) for different rolls: Roll Result Roll Results -1 2 -100 3 200 8 -100 9 -50 10 25 5 50 11 25 6 25 7 25 12 10 What is the expected value of your turn? Note that different possbilities of roll (sum of the upface of the two dices) does not necessarily have the same proabablity occurrence. (a) 0.23 (b) 5 (c) 0.91 (d) 10.91 (e) -5.28

Explanation / Answer

Let X be the sum of the numbers, this can range from 2 to 12.

P (X = 2) = P {(1,1)} = 1/36

P (X = 3) = P {(1,2), (2,1)} = 2/36

P (X = 4) = P ({(1,3), (3,1), (2,2)} = 3/36

P (X = 5) = P ({(1,4), (4,1), (2,3), (3,2} = 4/36

P (X = 6) = P ({(1,5), (5,1), (4,2), (2,4), (3,3)} = 5/36

P (X = 7) = P {(1,6), (6,1), (2,5), (5,2), (3,4), (4,3)} = 6/36

P (X = 8) = P {(2,6), (6,2), (3,5), (5,3), (4,4)} = 5/36

P (X = 9) = P {(3,6), (6,3), (4,5), (5,4)} = 4/36

P (X = 10) = P {(4,6), (6,4), (5,5)} = 3/36

P (X = 11) = P {(5,6), (6,5)} = 2/36

P (X = 12) = P {(6,6)} = 1/36

expected value = -5.27778 which is approximately equals to -5.28

option(e)

Roll Result probability probability*Result 2 -100 0.027778 -2.77778 3 200 0.055556 11.11111 4 0 0.083333 0 5 -50 0.111111 -5.55556 6 25 0.138889 3.472222 7 25 0.166667 4.166667 8 -100 0.138889 -13.8889 9 -50 0.111111 -5.55556 10 25 0.083333 2.083333 11 25 0.055556 1.388889 12 10 0.027778 0.277778 Total -5.27778

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