Question

Suppose you play a game in which you charge someone $10 to roll two dice. If they get doubles (either two ones, two twos, two threes, etc.), then you pay them $50 (for a net profit of $ -40 to you). If they don’t get doubles, then you keep their $10. a. Write out a probability distribution for X, the net profit to you. b. What is the expected value of the game from your point of view?

Answer 1

X : Net Profit to you

X : -$40 ; if they get doubles;

X : $10 ; it they do not get a double.

Event space (highlighted doubles)

Dice 1	Dice 2
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

Number possible events when two dice are rolled : (6x6) = 36

Number of possible events of getting a double when two dice are rolled = 6

Probability of getting a double when two dice are rolled = 6/36 = 1/6

Probability of not getting a double = 1-Probability of getting a double = 1 - 1/6 = 5/6

Probability distribution of X:

X	P(X)
-40	1/6
10	5/6

Expected value of the game from your point of view : E(X)

Expected value of the game from your point of view = 10/6 = $1.6667