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:-71 centsStep-by-step explanation:The total number of balls is 2 + 10 + 30 = 42 ballsThe probability of getting gold marble[tex]P_g = 2/42 = 0.04762[/tex]The probability of getting silver marble[tex]P_s = 10/42 = 0.2381[/tex]The probability of getting black marble[tex]P_b = 30/42 = 0.7143[/tex]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[tex]E = 5P_g + 2P_s - 2P_b[/tex][tex]E = 5*0.04762 + 2*0.2381 - 2*0.7143 = -0.714[/tex] dollaror -71 cents.So expect to lose 71 cents everytime you play this game