To find the theoretical probability of winning the prize, we need to determine how many winning outcomes there are compared to the total number of possible outcomes.
**Total outcomes**: The total number of outcomes is simply the total number of marbles in the bag. Since there are 12 marbles (4 green + 5 blue + 1 yellow + 2 orange), there are 12 possible outcomes.
**Winning outcomes**: The winning outcomes occur if you draw an orange or yellow marble. There are 2 orange marbles and 1 yellow marble, making for a total of 3 winning outcomes (2 orange + 1 yellow).
**Probability**: The probability is the ratio of winning outcomes to total outcomes. So the probability of drawing an orange or yellow marble is:
\[ \frac{3 \text{ winning outcomes}}{12 \text{ total outcomes}} = \frac{3}{12} = \frac{1}{4}. \]
Thus, the theoretical probability of winning the prize is \( \frac{1}{4} \).
