Math  /  Data & Statistics

QuestionIf you randomly select a letter from the phrase "Do not run on Ichiro," what is the probability that a vowel is randomly selected? Leave your answer as a reduced fraction.) \square

Studdy Solution

STEP 1

1. The phrase "Do not run on Ichiro" includes the letters: D, o, n, o, t, r, u, n, o, n, I, c, h, i, r, o.
2. Vowels are defined as the letters: a, e, i, o, u (considering both uppercase and lowercase).
3. The probability of selecting a vowel is the ratio of the number of vowels to the total number of letters in the phrase.
4. We must count the total number of letters and the number of vowels in the phrase.

STEP 2

1. Count the total number of letters in the phrase.
2. Count the number of vowels in the phrase.
3. Calculate the probability as the ratio of the number of vowels to the total number of letters.
4. Simplify the fraction to its lowest terms.

STEP 3

Count the total number of letters in the phrase "Do not run on Ichiro".
Total letters=17 \text{Total letters} = 17

STEP 4

Identify and count the vowels in the phrase. The vowels in the phrase are 'o', 'o', 'u', 'o', 'i', 'o'.
Number of vowels=6 \text{Number of vowels} = 6

STEP 5

Calculate the probability of selecting a vowel by dividing the number of vowels by the total number of letters.
Probability=Number of vowelsTotal number of letters=617 \text{Probability} = \frac{\text{Number of vowels}}{\text{Total number of letters}} = \frac{6}{17}

STEP 6

Simplify the fraction to its lowest terms if necessary. In this case, 617\frac{6}{17} cannot be simplified further as 6 and 17 have no common factors other than 1.
Simplified Probability=617 \text{Simplified Probability} = \frac{6}{17}
Solution: The probability that a vowel is randomly selected from the phrase "Do not run on Ichiro" is 617\frac{6}{17}.

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