The first step is to find the probability for each of the events, which are pick up a gold marble, pick up a silver marble and pick up a black marble:
[tex]\begin{gathered} P(G)=\frac{2}{36}=\frac{1}{18} \\ P(S)=\frac{8}{36}=\frac{2}{9} \\ P(B)=\frac{26}{36}=\frac{13}{18} \end{gathered}[/tex]Now, multiply each of the probabilities by its corresponding reward and find the sum of them to find the expected value:
[tex]\begin{gathered} E=3\cdot\frac{1}{18}+2\cdot\frac{2}{9}-1\cdot\frac{13}{18} \\ E=-0.11 \end{gathered}[/tex]The expected value is -$0.11.
