The following game has a $10 entry fee. You are to flip a fair coin three times. The first time it comes up heads you are paid $5. The second time it comes up heads you're paid an additional $7. The third time it comes up heads you're paid $9 more, for a possible maximum prize of $21. Would you pay the $10 entry fee to play?
If not, what would be a fair price for this game? Click below for the answer.
It's not a good idea to play this game at the offered entry fee. Here are the eight possible outcomes when flipping a coin three times, along with how much you would win after each flip.
When you subtract out the $10 entry fee, you only win "big" ($11) one out of eight times. Three times you win only $2, three times you lose $5, and one out of the eight times you lose your entire $10 entry fee. If you average these, you can expect to lose $1 every time you play. So, if you lower the entry fee to $9 this would be a fair game.
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