Question 944326
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?
<pre>
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
-----------------------------
  Expectation = &#931;(W*P) = -2/6 = -1/3 of a dollar.

The expectation is to lose {{{1/3}}} of a dollar or {{{33&1/3}}}¢ loss
per game on the average.  So it is not fair, because the expectation
is not 0.

Edwin</pre>