.
Total marbles = 3 + 8 + 20 = 31.
The probability to get a gold marble = .
The probability to get a silver marble = .
The probability to get a black marble = .
Now write and evaluate the expression for the Math expectation
E = = = of a dollar.
ANSWER. Math expectation is 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". |
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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.