From the word PROBABILITY (11 letters), one letter is chosen uniformly at random. What is the probability that the chosen letter is a vowel?

Introduction / Context:
We select one character uniformly from a word and ask for the chance it is a vowel. Repetitions matter in counting because each occurrence is a distinct favourable outcome.

Given Data / Assumptions:

• Word: PROBABILITY.
• Total letters = 11.
• Vowels among English letters: a, e, i, o, u.

Concept / Approach:
Count total characters and the number of vowel occurrences (including duplicates). Probability = vowel count / 11.

Step-by-Step Solution:
Letters with multiplicities: P(1), R(1), O(1), B(2), A(1), I(2), L(1), T(1), Y(1).Vowels present (with counts): A(1), O(1), I(2) → 4 vowels.Probability = 4/11.

Verification / Alternative check:
Consonant count = 7; 4 + 7 = 11 confirms total.

Why Other Options Are Wrong:
3/11 or 2/11 undercount vowel multiplicities; 0 ignores vowels entirely.

Common Pitfalls:
Counting distinct vowel types instead of occurrences; duplicates (I appears twice) must be included.

Final Answer:
4/11