Given
7 red
8 green
12 black
9 yellow
7+8+12+9 = 36 total balls.
The probability of getting 1 green and 1 yellow without replacement is
[tex]\begin{gathered} P(GY)=\frac{\text{number of green}}{\text{total number of balls}}\cdot\frac{\text{number of yellow}}{\text{total number of balls LEFT}} \\ \\ P(GY)=\frac{\text{8}}{36}\cdot\frac{9}{35} \\ P(GY)=\frac{72}{1260} \\ P(GY)=\frac{2}{35} \end{gathered}[/tex]Therefore, the probability is 2/35.
