The following describes a dice game played at a carnival. The game costs $5 to play. You roll the die once. If you roll a one or a two, you get nothing. If you roll a three or a four, you get $4 back. If you roll a five you get your $5 back and if you roll a six, you receive $12. What is your Expected Value? Should you play the game?
Since, E(x) = -5/6 = -0.83
Because the expected value is a negative answer, we'd say that the game is NOT fair. In the long run, players of this game will lose money. A fair game would yield an expected value of zero. So, now that we've calculated expected value and we know it's negative, how do we interpret this? The expected value of this problem could be interpreted as: If you were to play the game one time each week over a six-week period (and each time get a different outcome (1-6)), your _average_ loss would be $0.83 per play.
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