SOLUTION: If a player rolls two dice and a gets a sum of 2 or 12, she wins $20. If a person gets a product of 12, she wins $ 15. If she gets a sum of 5 or 9, she wins $2. For the game to be

The full space of events is the set of all pairs  (i,j), where i and j are integer numbers from 1 to 6, inclusively.

This space consists of  6*6 = 36 elements, and each element/event has the probability of  .


Of them, the outcomes where the sum is 2 or 12, are

    sum   2 :  (1,1)            In all, 1 pair worth $20.

    sum  12 :  (6,6)            In all, 1 pair worth $20.



The outcomes where the product is 12, are

                (2,6), (3,4), (4,3), (6,2)         In all, 4 pairs worth $15 each


The outcomes where the sum is 5 or 9, are


    sum 5 :  (1,4), (2,3), (3,2), (4,1)            In all, 4 pairs worth $2 each

    sum 9 :  (3,6), (4,5), (5,4), (6,3)            In all, 4 pairs worth $2 each



Thus the mathematical expectation of winning sum is


     =  =  =   =  dollars.



ANSWER.  For the game to be fair, the person should pay  dollars.