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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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The expected value of the game E = 4*P(gold) + 2*P(silver) - 1*P(black) dollars.
P(gold) = = .
P(silver) = .
P(black) = .
Therefore, the expected value of the game E = = = = of a dollar.
It means that you are expected to win of the dollar every time (in average) as you play the game.
Solved and explained.