Question

A bag contains 1 gold marbles, 9 silver marbles, and 24 black marbles. Someone offers to...

A bag contains 1 gold marbles, 9 silver marbles, and 24 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?

Math   Statistics-And-Probability   
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Answer #1

Solution:

We are given that a bag contains 1 gold marbles, 9 silver marbles, and 24 black marbles. Therefore, there are total 34 marbles in a bag.

The probability of selecting a gold marble is:

The probability of selecting a silver marble is:

The probability of selecting a black marble is:

We are also given that if it is gold you win $4. If it is silver, you win $2. If it is black, you lose $1.

We know that the expected value is:

  

  

Therefore, the expected value is -$0.0588

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