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A bag contains 2 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 $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 :

The expected value on playing this game is -5/36.

Given: 2 gold marbles, 9 silver marbles, and 24 black marbles.If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1.

To find: Expected value on playing the game

Chance of occurrence of  gold = 1/36

Chance of occurrence of silver = 9/36

Chance of occurrence of  black = 26/36

On multiplying the given probability of occurence with the amount you would lose or win

we get,

1/36 * 3 + 9/36 * 2 - 26/36 * 1

3/36 + 18/36 - 26/36

=$ -5/36

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