SOLUTION: A bag contains 3 gold marbles, 8 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If

Algebra ->  Probability-and-statistics -> SOLUTION: A bag contains 3 gold marbles, 8 silver marbles, and 20 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win $3. If       Log On


   

Question 1200352: A bag contains 3 gold marbles, 8 silver marbles, and 20 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?
$
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

Total marbles = 3 + 8 + 20 = 31.


The probability to get a gold   marble = 3%2F31.

The probability to get a silver marble = 8%2F31.

The probability to get a black  marble = 20%2F31.


Now write and evaluate the expression for the Math expectation

    E = 3%2A%283%2F31%29+%2B+2%2A%288%2F31%29+-+1%2A%2820%2F31%29 = %283%2A3+%2B+2%2A8+-+1%2A20%29%2F31 = 5%2F31  of a dollar.


ANSWER.  Math expectation is  5%2F31  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".                   |
    +----------------------------------------------------------------+


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.