SOLUTION: In a dice game, you roll a dice once for a $5 wager. You win $8.00 for rolling a 3 or a 4, and lose the original wager otherwise. What is your expected gain in this game?

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Question 516952: In a dice game, you roll a dice once for a $5 wager. You win $8.00 for rolling a 3 or a 4, and lose the original wager otherwise. What is your expected gain in this game?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
In a dice game, you roll a dice once for a $5 wager. You win $8.00 for rolling a 3 or a 4, and lose the original wager otherwise. What is your expected gain in this game? 
I will assume you get to keep your $5 wager if you win.  (If not the
8 must be replaced by 3)

Winnings   Probability   
   X           P(X)          X*P(X)
----------------------------------------- 
   8        2/6 = 1/3     8(1/3) =   8/3
  -5        4/6 = 2/3    -5(2/3) = -10/3
-----------------------------------------
                            Total = -2/3

You expect to average a loss of 2/3 of a dollar or 66%262%2F3 cents per game,
if you played it many times.

Edwin