1. **State the problem:** We want to find the experimental probability that the mouse walks into the red door based on the recorded frequencies. 2. **Recall the formula for experimental probability:** $$\text{Experimental Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}}$$ 3. **Identify the values:** - Number of favorable outcomes (red door frequency) = 22 - Total number of trials = 13 (black) + 15 (white) + 22 (red) = 50 4. **Calculate the probability:** $$\text{Probability of red door} = \frac{22}{50}$$ 5. **Simplify the fraction:** $$\frac{22}{50} = \frac{\cancel{2} \times 11}{\cancel{2} \times 25} = \frac{11}{25}$$ 6. **Interpretation:** The experimental probability that the mouse walks into the red door is $\frac{11}{25}$, which means out of every 25 trials, the mouse chooses the red door about 11 times on average. **Final answer:** $$\boxed{\frac{11}{25}}$$