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^n}}}, where as if the roll is not a prime number (1,4,6), the player pays Larry {{{n^2}}}. 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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