Question 1184817: Suppose it costs $6.00 to roll a pair of dice. You get paid the large number in dollars that appears on the dice unless you roll a double in which case you get paid the sum in dollars. If you play long enough for this game, are you expecting to win money or lose money? Is it a fair game?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! probability of a double is 1/36
if 1-1, the pay out is $2, and the expected gain is $2/36
if 2-2, the pay out is $4,and the expected gain is $4/46
if 3-3, the pay out is $6,and the expected gain is $6/36
if 4-4, the pay out is $8, $8/36
If 5-5 the pay out is $10, $10/36
if 6-6 the pay out is $12, $12/36
There are 30 other possibilities:
1-2/1-3/1-4/1-5/1-6 The gain is $20/36
2-1/2-3/2-4/2-5/2-6/ The expected gain is $20/36
3-1/3-2/3-4/3-5/3-6 will be $21/26
4-1/4-2/4-3/4-5/4-6/ will be $23/36
5-1/5-2/5-3/5-4/5-6/will be $26/36
6-1/6-2/6-3/6-4/6-5/will be $30/36
The expected gains are (2+4+6+8+10+12+140)/36
=$182/36, or $5.06
The loss is $6
The expected value is -$0.94, lose money, not a fair game
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