The letter tiles are W, I, S, D, O, and M.
First, we identify the vowels among these letters. The vowels in the English alphabet are A, E, I, O, U. From the letters present, we have:
- I
- O
So there are 2 vowels (I and O) in the set of tiles.
Next, we count the total number of letter tiles:
- Total letters = 6 (W, I, S, D, O, M)
Now, we calculate the probability of picking a vowel:
\[ \text{Probability} = \frac{\text{Number of favorable outcomes (vowels)}}{\text{Total number of outcomes (total letters)}} \]
This gives us:
\[ \text{Probability} = \frac{2}{6} \]
To simplify this fraction, we divide the numerator and the denominator by 2:
\[ \frac{2}{6} = \frac{1}{3} \]
Therefore, the probability that the letter Abby picks is a vowel is
\[ \boxed{\frac{1}{3}}. \]