Question 381488: Suppose you have a set of three four sided dice. Your friend wants to bet that he/she can roll the number combination 1,2,3 (any combination i.e. no die shows a four, and no die duplicates another). She/he wants to roll the dice one hundred times and each time the combination 1,2,3 comes up you will give him/her one dollar, each time it does not come up she/he will give you 10 cents. How much would you expect to win or lose based on statistically theory.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose you have a set of three four sided dice. Your friend wants to bet that he/she can roll the number combination 1,2,3 (any combination i.e. no die shows a four, and no die duplicates another). She/he wants to roll the dice one hundred times and each time the combination 1,2,3 comes up you will give him/her one dollar, each time it does not come up she/he will give you 10 cents. How much would you expect to win or lose based on statistically theory.
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# of ways to get 1,2,3: 3*2*1 = 6
# of possible outcomes: 6^3 = 216
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P(getting 1,2,3) = 6/216 = 3/108 = 1/36
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Expected winnings for me = (-10)(1/36) + (0.10)(35/36)
= [-10+3.5]/36
= -0.18
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I can expect to lose 18 cents each time the dice are thrown.
I can expect to lose $18 in 100 throws of the dice.
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Cheers,
Stan H.
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