Question 1200352
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Total marbles = 3 + 8 + 20 = 31.


The probability to get a gold   marble = {{{3/31}}}.

The probability to get a silver marble = {{{8/31}}}.

The probability to get a black  marble = {{{20/31}}}.


Now write and evaluate the expression for the Math expectation

    E = {{{3*(3/31) + 2*(8/31) - 1*(20/31)}}} = {{{(3*3 + 2*8 - 1*20)/31}}} = {{{5/31}}}  of a dollar.


<U>ANSWER</U>.  Math expectation is  {{{5/31}}}  of a dollar.


It is an infinitely long decimal, but it should not embarrass you: 


    +----------------------------------------------------------------+
    |   it is NOT what you win - it is only the MEAN VALUE to win    |
    |        after playing this game infinitely many times,          |
    |             so, it is an  "abstract number".                   |
    +----------------------------------------------------------------+


If you want, you may round this value to the closest cent, but it is not necessary - 

- it depends only on your wish or on the problem's requirement.


Since this problem wants the answer in dollars, you can round it to nearest cent.
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