SOLUTION: Larry made up a dice game. The rules state that if the roll, n is a prime number (2,3,5), then Larry will pay the player {{{2^n}}}, where as if the roll is not a prime number (1,4,

Algebra ->  Probability-and-statistics -> SOLUTION: Larry made up a dice game. The rules state that if the roll, n is a prime number (2,3,5), then Larry will pay the player {{{2^n}}}, where as if the roll is not a prime number (1,4,      Log On


   

Question 769798: Larry made up a dice game. The rules state that if the roll, n is a prime number (2,3,5), then Larry will pay the player 2%5En, where as if the roll is not a prime number (1,4,6), the player pays Larry n%5E2. Determine the probability distribution and determine the expectation of winning for this game. Please show all the work to get to the answer.
Answer by oscargut(2103) About Me  (Show Source):
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Larry made up a dice game. The rules state that if the roll, n is a prime number (2,3,5), then Larry will pay the player 2%5En, where as if the roll is not a prime number (1,4,6), the player pays Larry n%5E2. Determine the probability distribution and determine the expectation of winning for this

Here is the work
Let W = winning
If n = 1 then the player pays larry 1 ( W = -1)
If n = 4 then the player pays larry 16 ( W = -16)
If n = 6 then the player pays larry 36 ( W = -36)
If n = 2 then larry pays to the player 4 ( W = 4)
If n = 3 then larry pays to the player 8 ( W = 8)
If n = 5 then larry pays to the player 32 ( W = 32)
Then the distribution of W is:
P(W = -1)=P(W=-16)=P(W=-36)=P(W=4)=P(W=8)=P(W=32)
EXpected value of W is: (-1-16-36+4+8+32)/6 = -9/6 = -1.5
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