A bag contains 3 gold marbles, 6 silver marbles, and 30 black marbles. The rules of the game are as follows: You randomly select one marble from the bag. If it is gold, you win $6, if it is silver, you win $5. If it costs $1 to play, what is your expected profit or loss if you play this game?

Answer:The expected profit is $0.23077.Step-by-step explanation:From the given information it is clear thatGold marbles = 3Silver marbles = 6Black marbles = 30Total number of marbles = 3+6+30=39The probability of selecting gold marble is[tex]\frac{3}{39}=\frac{1}{13}[/tex]The probability of selecting silver marble is[tex]\frac{6}{39}=\frac{2}{13}[/tex]The probability of selecting black marble is[tex]\frac{30}{39}=\frac{10}{13}[/tex]It is given that If it is gold, you win $6, if it is silver, you win $5. If it costs $1 to play. Then the expected profit isExpected profit or loss = 6(Probability of gold marble)+5(Probability of silver marble)-1Expected profit or loss = [tex]6(\frac{1}{13})+5(\frac{2}{13})-1[/tex]Expected profit or loss = [tex]\frac{6}{13}+\frac{10}{13}-1[/tex]Expected profit or loss = [tex]\frac{6+10-13}{13}[/tex]Expected profit or loss = [tex]\frac{3}{13}[/tex]Expected profit or loss = 0.23076923Expected profit or loss ≈ 0.23077Positive sigh represents the profit.Therefore the expected profit is $0.23077.