SOLUTION: If a fair die rolled once comes up 6 you win $100. Otherwise, you lose $15. Would a rational person play this game? Justify your answer, using the definition of E(X).

Question 347790: If a fair die rolled once comes up 6 you win $100. Otherwise, you lose $15. Would a rational person play this game? Justify your answer, using the definition of E(X).
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If a fair die rolled once comes up 6 you win $100. Otherwise, you lose $15. Would a rational person play this game? Justify your answer, using the definition of E(X).
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Probability of rolling a 6: 1/6
Probability of not rolling a 6: 5/6
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E(x) = (1/6)*100 + (5/6)(-15)
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E(x) = (100 - 75)/6 = 25/6 = $4.17
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The player can expect to win $4.17 each time he/she plays the game.
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Cheers,
Stan H.
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