A bag contains 4 gold marbles, 8 silver marbles, and 26 black marbles. Someone offers to play this game: You randomly select one marble from the bag. If it is gold, you win \( \$ 3 \). If it is silver, you win \( \$ 2 \). If it is black, you lose \( \$ 1 \). What is your expected value if you play this game? Round your answer to two decimal places.

To calculate the expected value, we first need to identify the total number of marbles in the bag, which is \(4 + 8 + 26 = 38\) marbles. Next, we calculate the probabilities for each type of marble: - Probability of drawing a gold marble: \(\frac{4}{38} = \frac{2}{19}\) - Probability of drawing a silver marble: \(\frac{8}{38} = \frac{4}{19}\) - Probability of drawing a black marble: \(\frac{26}{38} = \frac{13}{19}\) Now we calculate the expected value (EV) by multiplying each outcome with its probability: - EV from gold marbles: \(\frac{2}{19} \times 3 = \frac{6}{19}\) - EV from silver marbles: \(\frac{4}{19} \times 2 = \frac{8}{19}\) - EV from black marbles: \(\frac{13}{19} \times (-1) = -\frac{13}{19}\) Now we sum these expected values: \[ EV = \frac{6}{19} + \frac{8}{19} - \frac{13}{19} = \frac{1}{19} \] To convert this into a decimal: \[ \frac{1}{19} \approx 0.0526 \] Rounding to two decimal places gives us: \[ \text{Expected Value} \approx 0.05 \] So, the expected value if you play this game is approximately \$0.05.