1. **State the problem:** We have a bag with eight tiles labeled F, G, H, I, J, K, L, and M. We want to find the probability of picking a vowel. 2. **Identify vowels:** The vowels in the English alphabet are A, E, I, O, U. From the tiles, the only vowel is I. 3. **Total number of tiles:** There are 8 tiles in total. 4. **Number of favorable outcomes:** Only 1 tile (I) is a vowel. 5. **Probability formula:** The probability of an event is given by $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ 6. **Apply the formula:** $$\text{Probability of picking a vowel} = \frac{1}{8}$$ 7. **Final answer:** The probability of picking a vowel from the bag is $\frac{1}{8}$.