a person pays $2 to play a certain game by rolling a single die once. if a 1 or
2 comes up the person wins nothing. if, however they roll a 3,4,5, 0r 6, the
player wins the difference between the number rolled and $2. Find the the
expectation for this game. is the game fair?
Roll Winnings Prob. W*P
1 -2+0=-2 1/6 -2/6
2 -2+0=-2 1/6 -2/6
3 -2+1=-1 1/6 -1/6
4 -2+2= 0 1/6 0
5 -2+3= 1 1/6 1/6
6 -2+4= 2 1/6 2/6
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Expectation = Σ(W*P) = -2/6 = -1/3 of a dollar.
The expectation is to lose of a dollar or ¢ loss
per game on the average. So it is not fair, because the expectation
is not 0.
Edwin