From a set of 26 balls labeled with the letters A to Z, one ball is selected at random. What is the probability that the chosen ball corresponds to a vowel letter (A, E, I, O or U)?

Introduction / Context:
The question tests a very basic probability idea where all outcomes are equally likely. We have balls labeled with letters of the English alphabet, and we want the probability that a randomly selected ball shows a vowel. Such questions help learners get comfortable with counting favorable outcomes and dividing by the total number of equally likely outcomes. This kind of problem is often used as the starting point for more advanced probability ideas.

Given Data / Assumptions:

• There are 26 balls in total, each labeled with a distinct letter from A to Z.
• The vowel letters considered are A, E, I, O and U, so there are 5 vowels.
• One ball is chosen at random and every ball is equally likely to be selected.
• No additional structure such as replacement is involved, because only one ball is drawn.

Concept / Approach:
The core concept is classical probability. For equally likely outcomes, the probability of an event is defined as favorable outcomes divided by total outcomes. Here, favorable outcomes correspond to balls that carry a vowel letter. Total outcomes correspond to all available balls. We only need to count how many balls correspond to vowels and how many balls there are in total.

Step-by-Step Solution:
Step 1: Count the total number of balls, which is 26.Step 2: Count the vowel letters among A to Z. The vowels are A, E, I, O and U, which gives 5 vowels.Step 3: The number of favorable outcomes is therefore 5, one for each vowel labeled ball.Step 4: Use the probability formula probability = favorable outcomes / total outcomes.Step 5: Substitute values to get probability = 5 / 26.Step 6: There is no need to simplify further because 5 and 26 have no common factor other than 1.
Verification / Alternative check:
We can verify the count by listing vowels explicitly. The alphabet has letters A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y and Z. Among these, A, E, I, O and U are exactly 5 vowels. All letters are distinct, and each ball is equally likely, so the classical probability approach is valid and leads naturally to 5/26. There is no other subtle condition in the problem, so the calculation is consistent.

Why Other Options Are Wrong:
21/26 is the probability of selecting a consonant, not a vowel. 10/26 corresponds to double counting the vowels, which has no justification in the scenario. 1/26 would be the probability if there were only one vowel, which is incorrect. 11/26 does not match any reasonable count of vowels or consonants and does not arise from correct counting.

Common Pitfalls:
Students sometimes forget that there are 5 vowels in the English alphabet and may accidentally include Y, which would change the count. Another common error is to mix up the probability of selecting a vowel with the probability of selecting a consonant and pick the complement instead. Learners may also try to overcomplicate this very simple scenario by imagining multiple draws when only one ball is selected.

Final Answer:
The correct probability that a randomly selected ball shows a vowel letter is 5/26.