Originally Posted by

**hollymxox** Hey,

could you please review my solution for the second question I asked?

Jason has designed a game 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 must pay the value of the roll.

a. what is the expected value [E(x)] per roll?

2, 3, 5, 7, and 11 are prime, 4, 6, 8, 9, 10, and 12 are composite.

Let X be the variable of the net value of each roll. So if, for instance, you roll a 5, X is 10, but if you roll a 6, X is -6.

is it correct to do it by making this table?

. X ... p(X) .... X*p(X)

-12 ... 1/36 ... -12/36

-10 ... 3/36 ... -30/36

-9 ..... 4/36 ... -36/36

-8 ..... 5/36 ... -40/36

-6 ..... 5/36 ... -30/36

-4 ..... 3/36 ... -12/36

4 ...... 1/36 ... 4/36

6 ...... 2/36 ... 12/36

10 .... 4/36 ... 40/36

14 .... 6/36 ... 84/36

22 .... 2/36 ... 44/36

Add up the third column to get E(X) = 24/36 = 2/3

b. The game is not fair since E(X) is not equal to zero.