There are 7 tiles labeled $A, B, C, D, E, F, G$.

Out of these, the vowels are $A$ and $E$, which are 2 vowels.

The probability of picking a vowel is calculated by dividing the number of favorable outcomes (the vowels) by the total number of tiles.

$\text{Probability} = \frac{\text{Number of vowels}}{\text{Total number of tiles}} = \frac{2}{7}$

Thus, the probability of picking a vowel is $\frac{2}{7}$.

Would you like further details or clarification on any part of this?

Here are some related questions you might find helpful:

1. What is the probability of picking a consonant?
2. If two tiles are picked without replacement, what is the probability that both are vowels?
3. What is the probability of picking a tile that is not a vowel?
4. If one tile is picked and replaced, what is the probability of picking a vowel on the second pick?
5. How would the probability change if another vowel was added to the bag?

Tip: When calculating probability, always ensure the total number of possible outcomes is correctly accounted for.