When two fair dice are rolled, there are 36 possible outcomes, each with the probability of  .


These outcomes are the pairs of integer numbers (i,j), where i and j take independently the values from 1 to 6.


The number of such pairs with the sum i+j = 7 is  6

( the pairs are (1,6), (2,5), (3,4), (4,3), (5,2) and (6,1) ).


So, the probability to get the sum of 7 at each roll of a pair of dice is   = .


Mathematical expectation of the amount of money to win at each roll of a pair of dice is   dollars,
but Joe should pay one dollar for each roll,

so his expected profit at each roll of a pair of dice is


     =  =   of a dollar.


Thus, statistically, Joe should expect the loss   of a dollar in each roll of a pair of dice.


Making 15 rolls in the game, Joe should expect to lose   dollars =  dollars = $2.50.     ANSWER