Question 1156437
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The total number of marbles is  3+10+29 = 42.


The expected <U>value</U> of the game is


    expected value = {{{6*(3/42)}}} + {{{2*(10/42)}}} - 1 = {{{18/42}}} + {{{20/42}}} - 1 = {{{38/42}}} - 1 = {{{(38-42)/42}}} = {{{-4/42}}} = {{{-1/13}}}  dollars.


<U>ANSWER</U>.  Expected <U>loss</U>  of the gamer is  {{{1/13}}}  dollars.

         It means that if the gamer plays this game many times, he or she will lose  {{{1/13}}}  of the dollars in average per game.
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Solved.