Question 1138185
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When two fair dice are rolled, there are 36 possible outcomes, each with the probability of  {{{1/36}}}.


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  {{{6/36}}} = {{{1/6}}}.


Mathematical expectation of the amount of money to win at each roll of a pair of dice is  {{{5*(1/6)}}} dollars,
but Joe should pay one dollar for each roll,

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


    {{{5*(1/6) - 1}}} = {{{5/6-1}}} = {{{-1/6}}}  of a dollar.


Thus, statistically, Joe should expect the loss  {{{1/6}}} of a dollar in each roll of a pair of dice.


Making 15 rolls in the game, Joe should expect to lose  {{{15*(1/6)}}} dollars = {{{5/2}}} dollars = $2.50.     <U>ANSWER</U>
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