To find the theoretical probability of picking a green marble, we first need to determine the total number of marbles in the bag.
- Pink marbles: 5
- Red marbles: 7
- Green marbles: 12
- Blue marbles: 2
- Black marbles: 4
Now we can calculate the total number of marbles:
\[ 5 + 7 + 12 + 2 + 4 = 30 \]
Next, the number of green marbles is 12. The probability of picking a green marble is calculated as the ratio of the number of green marbles to the total number of marbles:
\[ P(\text{Green}) = \frac{\text{Number of Green Marbles}}{\text{Total Number of Marbles}} = \frac{12}{30} \]
Now, we can simplify this fraction:
\[ \frac{12}{30} = \frac{2}{5} \]
Thus, the theoretical probability of picking a green marble is:
\[ \frac{2}{5} \]
So, the correct response is:
Start Fraction 2 over 5 End Fraction