Question 1205001
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A bag contains 1 gold marbles, 10 silver marbles, and 29 black marbles. Someone offers 
to play this game: You randomly select one marble from the bag. 
If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.
What is your expected value if you play this game?
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In total, there are 1 + 10 + 29 = 40 marbles.


mathematical expectation = {{{3*(1/40) + 2*(10/40) - 1*(29/40)}}} = {{{(3 + 20 - 29)/40}}} = {{{-6/40}}} = {{{-3/20}}} = -0.15 of a dollar, or -15 cents.


If you play this game many times, you will lose about 15 cents per game, in average.
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Solved.