To calculate the theoretical probability of picking a green marble from the bag, we first need to find the total number of marbles.
The total number of marbles is:
- Pink: 5
- Red: 7
- Green: 12
- Blue: 2
- Black: 4
Total = 5 + 7 + 12 + 2 + 4 = 30 marbles
The number of green marbles is 12.
The probability \( P \) of picking a green marble is calculated using the formula:
\[ P(\text{Green}) = \frac{\text{Number of Green Marbles}}{\text{Total Number of Marbles}} = \frac{12}{30} \]
Now, we can simplify \( \frac{12}{30} \):
\[ P(\text{Green}) = \frac{12 \div 6}{30 \div 6} = \frac{2}{5} \]
The theoretical probability of picking a green marble is \( \frac{2}{5} \).
Looking at the given responses, the correct one is not listed, but it seems “\( \frac{3}{5} \)” might be a misunderstanding or typo in choices.
To summarize:
- Total marbles: 30
- Green marbles: 12
- Theoretical probability of picking a green marble: \( \frac{2}{5} \)