Question 1203844: A bag contains 1 gold marbles, 8 silver marbles, and 21 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?
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
X = net winnings
| Color | X | P(X) | | Gold | 4 | 1/30 | | Silver | 2 | 8/30 | | Black | -1 | 21/30 |
Form a new column in which we multiply each X and P(X) value.
| Color | X | P(X) | X*P(X) | | Gold | 4 | 1/30 | 4/30 | | Silver | 2 | 8/30 | 16/30 | | Black | -1 | 21/30 | -21/30 |
Add up the results of that last column to get the expected value.
4/30 + 16/30 + (-21/30)
=(4+16-21)/30
=-1/30
=-0.03 approximately
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Answer: -0.03 dollars
It means you should expect to lose 3 cents, on average, each time you play the game.
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