Question

You play a game in which two dice are rolled. If a sum of 7 appears, you win ten dollars; otherwise, you lose two. If you intend to play this game for a long time, should you expect to make money, lose money, or come out about even? Explain.

Answer 1

Come out even

Explanation:

The total numbers of faces in rolling two dice = 6 X 6 = 36

The sum of appears in the following cases: {6, 1}, {1, 6}, {2, 5}, {5, 2}, (3, 4}, {4, 3}. Making a total of 6 cases

Probability of obtaining a sum of 7 = possible number of cases where the sum of 7 appears ÷ total number of outcome

= 6/36 = 1/6

Probability of not obtaining a sum of 7 = 1 - Probability of obtaining a sum of 7

= 1 - 1/6

= 5/6

Expected Value: (1/6)10 + (5/6)(-2) = (10-10)/6 = 0

So the answer is come out even