When rolling two dice, in all, 36 equally likely outcomes are possible.


Of them, there are 2 outcomes that produce the sum of 11 :  (5,6) and (6,5).


Also, there are 6 outcomes that produce the sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1).


So, you can win $20 with the probability    and

    you can win  $5 with the probability  .


So, your winning expectation is   =  =  = 1.94  dollars.


From it, you should subtract the cost of the play of $3,  so the expectation of the game is  $1.94 - $3.00 = - $1.06.


In other words, you will lose 1.06 dollars statistically at each game, in average.