Answer:
-71 cents
Step-by-step explanation:
The total number of balls is 2 + 10 + 30 = 42 balls
The 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] dollar
or -71 cents.
So expect to lose 71 cents everytime you play this game
