A bag contains 1 gold marbles, 10 silver marbles, and 21 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?

Answer:The expected value is -0.5625.Step-by-step explanation:Given,Gold marbles = 1,Silver marbles = 10,And, black marbles = 21,Thus, the total marbles = 1 + 10 + 21 = 32,So, the probability of gold marble = [tex]\frac{\text{ gold marble}}{\text{total marbles}}=\frac{1}{32}[/tex]Similarly, probability of silver marble = [tex]\frac{10}{32}[/tex]Probability of black marble = [tex]\frac{21}{32}[/tex]Now, the value of a gold marble, a silver marble and black marble are $4, $2 and - $2 respectively, ( -$ 2 means loss of $ 2 )So, expected value of gold = probability of a gold marble × the value of a gold marble = [tex]4(\frac{1}{32})[/tex]Similarly,Expected value of silver marble = [tex]2(\frac{10}{32})[/tex]Expected value of black marble = [tex]-2(\frac{21}{32})[/tex]Hence, the total expected value =  [tex]4(\frac{1}{32})+2(\frac{10}{32})+-2(\frac{21}{32})[/tex][tex]=-0.5625[/tex]