SOLUTION: Hi, I am having a very hard time solving this stats problem and if someone could give me some assistance I would be ever greatful. The question is as follows. "There is a new game

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Question 428822: Hi, I am having a very hard time solving this stats problem and if someone could give me some assistance I would be ever greatful. The question is as follows. "There is a new game and a friend asks your advice on playing it. Like yahtzee, it is played with 5 fair sided dice. The game costs $1 to play. The player wins $50 for rolling a total greater than 27. What is your friends expected gain or loss for one play? Be sure to consider all possible cases" I am pretty sure that I should use a multinomial for this problem but I don't have any idea how to set it up. I would appreciate it very much if someone could run me through how to do it.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
"There is a new game and a friend asks your advice on playing it. Like yahtzee, it is played with 5 fair sided dice. The game costs $1 to play. The player wins $50 for rolling a total greater than 27. What is your friends expected gain or loss for one play?
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Throwing five 6-sided dice you can get 6^5 = 7776 different results.
You would have to count the number of results that have a sum
greater then 27; say that number is "x".
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Then the probability of winning is x/7776.
And probability of losing is [1-(x/7776)]
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Random gain values are: 49 and -1
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Expected gain is [49[x/7776]] + [-1[1-[x/7776]]
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Cheers,
Stan H.