SOLUTION: a player rolls a fair die and receives $2 if they roll a 2 and nothing if they don't roll a 2. If the game costs $1.25, how much should the player expect to win or lose over the lo

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Question 1135815: a player rolls a fair die and receives $2 if they roll a 2 and nothing if they don't roll a 2. If the game costs $1.25, how much should the player expect to win or lose over the long run?
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
If he wins, his net winning is only 75 cents because he paid
$1.25 to play, since $2.00-$1.25 = $0.75.  If he loses he
loses the $1.25 he paid to play, indicated by a negative
number.

  Roll          X     P(X)    E(X) = X∙P(X) 
--------------------------------------------         
    2        $0.75    1/6    ($0.75)(1/6) =  $0.125     
1,3,4,5,6   -$1.25    5/6   (-$1.25)(5/6) = -$1.041666667
                            -----------------------------  
                        Total expectation = -$0.916666667

So in the long run, he'll average losing about 92 cents a game.

Edwin