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One letter tile is randomly drawn from a set of $26$ alphabet tiles representing letters $A$ through $Z$ . What is the probability that the letter drawn is a vowel or is in the word ＂now＂ ( $y$ does not count as a vowel here)? Give your answer as a fraction in reduced form.

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Theoretical probability

Full solution

Q. One letter tile is randomly drawn from a set of

26

alphabet tiles representing letters

A

through

Z

. What is the probability that the letter drawn is a vowel or is in the word ＂now＂ (

y

does not count as a vowel here)? Give your answer as a fraction in reduced form.

Question Prompt: Question prompt: What is the probability of drawing a vowel or a letter from the word ＂now＂ from a set of $26$ alphabet tiles?
Identify Vowels: Identify the vowels in the alphabet: $A$ , $E$ , $I$ , $O$ , $U$ . That's $5$ vowels.
Identify Unique Letters: Identify the unique letters in the word ＂now＂: $N$ , $O$ , $W$ . That's $3$ letters.
Consider Overlapping: Notice that the letter O is both a vowel and in the word ＂now＂. We don't wanna count it twice, so we have $5$ vowels + $2$ other unique letters from ＂now＂ (N and W).
Calculate Favorable Outcomes: Calculate the total number of favorable outcomes: $5$ vowels $(A, E, I, O, U)$ + $2$ letters from ＂now＂ $(N, W)$ = $7$ favorable outcomes.
Calculate Probability: Calculate the probability: $P(\text{vowel or letter in ＂now＂}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{7}{26}$ .

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