Question

A player rolls two dice, and wins a number of dollars equal to the sum on the dice. What is the expected value of this game?Choose one answer. 1. 62. 73. 54. 8

Answer 1

In order to find the expected value, first let's list all the possible outcomes of rolling two dices:

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6).

The sum of the values in each outcome is given by:

2, 3, 4, 5, 6, 7,

3, 4, 5, 6, 7, 8,

4, 5, 6, 7, 8, 9,

5, 6, 7, 8, 9, 10,

6, 7, 8, 9, 10, 11,

7, 8, 9, 10, 11, 12.

Now, to calculate the expected value, let's add all values and divide by the number of values:

Therefore the correct option is 2. (expected value = 7)