1. **State the problem:** Mrs. Cox picks two marbles with replacement from a bag containing 5 blue, 4 red, and 3 orange marbles. We want the probability that neither marble picked is orange. 2. **Total marbles:** There are $5 + 4 + 3 = 12$ marbles in total. 3. **Probability of picking a non-orange marble in one draw:** Number of non-orange marbles = $5 + 4 = 9$. Probability = $\frac{9}{12} = \frac{3}{4}$. 4. **Since the marble is replaced, the draws are independent.** The probability of picking two non-orange marbles is the product of the probabilities of each draw: $$\left(\frac{3}{4}\right) \times \left(\frac{3}{4}\right) = \frac{3}{4} \times \frac{3}{4} = \frac{9}{16}.$$ 5. **Final answer:** The probability that Mrs. Cox picks two marbles that are not orange is $\boxed{\frac{9}{16}}$.