Question

one letter tile is drawn randomly from a set of 26 alphabet tiles representing letters a through z. what is the probability that the letter drawn is a vowel (a, e, i, o, u) or is in the word none? give your answer as a fraction in simplest form. ( y is not a vowel.)

a 1/26
b 4/13
c 3/13
d 1/13
e 1/26

Explanation:

Step1: Identify favorable outcomes

Vowels: A, E, I, O, U (5 letters). Word "none" has letters N, O, N, E. Unique letters: N, O, E. But O and E are already vowels. So new unique letter from "none" is N. So total favorable: 5 (vowels) + 1 (N) = 6? Wait, wait. Wait, "none" is N, O, N, E. So unique letters in "none" are N, O, E. O and E are vowels (O is vowel, E is vowel). So the letters that are vowel or in "none" are: vowels (A, E, I, O, U) plus N (since N is in "none" and not a vowel). Wait, let's list all: A, E, I, O, U (vowels) and N (from "none"). Wait, but "none" has E and O which are already vowels. So the set of letters that are vowel or in "none" is {A, E, I, O, U, N}. Wait, is that right? Let's check: vowel (A,E,I,O,U) or in "none" (N,O,N,E). So union is A, E, I, O, U, N. So that's 6 letters? Wait, no: A, E, I, O, U (5) and N (1) because O and E are already in vowels. So total favorable is 6? Wait, but the total number of alphabet tiles is 26 (A-Z). Wait, the problem says "a set of 26 alphabet tiles". So total possible outcomes: 26.

Wait, maybe I made a mistake. Let's re-express:

Vowels: A, E, I, O, U (5 letters).

Letters in "none": N, O, N, E. So unique letters: N, O, E.

Now, the union of vowels and letters in "none" is (vowels) ∪ (letters in "none") = {A, E, I, O, U} ∪ {N, O, E} = {A, E, I, O, U, N}. So that's 6 letters? Wait, no: A, E, I, O, U (5) and N (1) because O and E are already in vowels. So total elements: 5 + 1 = 6? Wait, no: {A, E, I, O, U, N} has 6 elements. Wait, but let's count: A, E, I, O, U, N. That's 6. Wait, but maybe I missed something. Wait, "none" is N, O, N, E. So O and E are vowels, N is not. So the letters that are vowel or in "none" are all vowels plus N. So that's 5 vowels + 1 (N) = 6. Wait, but let's check the answer options. The options include 6/26? Wait, 6/26 simplifies to 3/13? Wait, 6 divided by 26 is 3/13. Wait, one of the options is B. 6/26? Wait, no, the options are:

A. 12% (which is 3/25 ≈ 0.12, no)

B. 6/26 (which simplifies to 3/13 ≈ 0.23)

C. 3/13 (which is 6/26 simplified)

D. 1/3 (≈0.33)

E. 30% (0.3)

Wait, let's recalculate.

Wait, maybe I made a mistake in the favorable outcomes. Let's list all letters that are vowel or in "none":

Vowels: A, E, I, O, U (5)

Letters in "none": N, O, N, E. So unique letters: N, O, E.

Now, the union is vowels (A,E,I,O,U) plus N (since O and E are already in vowels). So the union is A, E, I, O, U, N. So that's 6 letters. Wait, but O and E are in both, so we don't double count. So the number of favorable outcomes is 6? Wait, but 6/26 simplifies to 3/13. Let's check the options. Option C is 3/13. So that's the answer.

Wait, let's verify:

Total possible: 26.

Favorable: letters that are vowel (A,E,I,O,U) or in "none" (N,O,E). So combining, we have A, E, I, O, U, N. That's 6 letters. So probability is 6/26 = 3/13. So option C is 3/13.

Step2: Calculate probability

Probability = number of favorable outcomes / total number of outcomes = 6/26 = 3/13.

Answer:

C. 3/13