Question

A bag of marbles contains 2 gold marbles, 10 silver marbles, and 30 black marbles. You decide to play the following game: Randomly select one marble from the bag. If it is gold, you win $5. If it is silver, you win $2. If it is black, you lose $2. What is the expected value if you play the game? Express losses as negative values and do not include the dollar sign in your answer. Round to the nearest cent.

Answer 1

Answer:

-.71

Step-by-step explanation:

Total Marbles: 2+10+30=42

Gold Marble: 2/42= 0.0476

Silver Marbles: 10/42= 0.238

Black Marbles: 30/42= 0.714

Answer 2

Answer:

-71 cents

Step-by-step explanation:

The total number of balls is 2 + 10 + 30 = 42 balls

The probability of getting gold marble$P_g = 2/42 = 0.04762$

The probability of getting silver marble$P_s = 10/42 = 0.2381$

The probability of getting black marble$P_b = 30/42 = 0.7143$

With the price for each case, we can calculate the expected value of the game by multiplying the price money by the probability and sum them up

$E = 5P_g + 2P_s - 2P_b$

$E = 5*0.04762 + 2*0.2381 - 2*0.7143 = -0.714$ dollar

or -71 cents.

So expect to lose 71 cents everytime you play this game