One letter is picked at random from the word PROBABILITY…

Step 1. Outcomes. P, R, O, B, A, B, I, L, I, T, Y: $11$ letters, so $11$ outcomes.

Step 2. B. There are two B's: $2$ outcomes. So $P(\text{B}) = \dfrac{2}{11}$.

Step 3. Vowels. O, A, I and I: $4$ outcomes. So $P(\text{vowel}) = \dfrac{4}{11}$.