A game has been designed where if you roll a prime number with two six-sided dice?

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Kelly B

New member
A game has been designed where if you roll a prime number with two six-sided dice, you receive twice the amount of your roll, but if you roll a composite number (not prime), you must pay the value of the roll. Prime numbers are only divisible by 1 or itself, composite numbers can also be divided by 2 and 3.

a.) What is the expected value per roll?
b.) Is this a fair game? Explain.

My answer:

The expected value per roll is 18.33 (prime) and 6.11 (non prime).

Prime:
X (value) P(x)
6 3/36
10 5/36
14 7/36
18 9/36
22 11/36

E(x) = (6x3/36)+ (10x5/36)+ (14x7/36)+ (18x9/36)+ (22x11/36) = 18.33

Composite:

X(value) P(x)
2 2/36
4 4/36
6 6/36
8 8/36
10 10/36

E(x) = (2x2/36)+ (14x4/36)+ (6x6/36)+ (8x8/36)+ (10x10/36) = 6.11

Is this correct?

Thanks for the help!
 
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