Question 1195583
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A bag contains 3 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 $4. 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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<pre>
The expected value of the game  E = 4*P(gold) + 2*P(silver) - 1*P(black)  dollars.


P(gold)   = {{{3/(3+10+29)}}} = {{{3/42}}}.

P(silver) = {{{10/42}}}.

P(black)  = {{{29/42}}}.


Therefore, the expected value of the game  E = {{{4*(3/42) + 2*(10/42) - 1*(29/42)}}} = {{{(4*3 + 2*10 - 29)/42}}} = {{{3/42}}} = {{{1/14}}}  of a dollar.


It means that you are expected to win  {{{1/14}}}  of the dollar every time (in average) as you play the game.
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Solved and explained.