A dice game lets you roll 2 6 sided disc and find the sum of the numbers. A 12 wins 100 dollars, 10 or 11 wins 50 dollars, a 2 wins 3 dollars. The game costs 6 dollars to play. What is th expected outcome of this game?

Question

Mathematics

Jaron Gross

23 July, 01:09

A dice game lets you roll 2 6 sided disc and find the sum of the numbers. A 12 wins 100 dollars, 10 or 11 wins 50 dollars, a 2 wins 3 dollars. The game costs 6 dollars to play. What is th expected outcome of this game?

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Answers (1)

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Scout · Answer 1

Step-by-step explanation:

A two 6 sided die is rolled

Sample space would be (1,1) ... (1,6) ... (6,1) ... (6,6)

Let x be the sum obtained

X can take values as 2 or 3 ... 12

P (x=12) = P (6,6) = 1/36

P (x=10 or 11) = P{ (5,5) (5,6) (6,5) (4,6) (6,4) }=5/36

P (2) = P (1,1) = 1/36

For other outcomes no payment

Thus we can list this as

Sum 2 3 4 5 6 7 8 9 10 or 11 12

Prob 1/36 5/36 1/36

Gain 3 0 0 0 0 0 0 0 50 100

E (gain) 3/36 0 0 0 0 0 0 0 250/36 100/36

E (gain) = total = 353/36

Cost of game = 6

E (outcome) = E (gain - 6) = E (gain) - 6 = 353/36 - 6

= 3.806