suppose you choose a letter at random from the word ARITHMETIC. What are the odds in favor of selecting a vowel? What are the odds against selecting a vowel?

The arithmetic post was already answered. Kim, please post a new question instead of "tagging" on the end of someone else's. 1/3 of a number can be written as 1/3x (or any other letter attached).

To find the odds in favor of selecting a vowel from the word ARITHMETIC, we need to determine the number of favorable outcomes (selecting a vowel) and divide it by the number of total outcomes (selecting any letter). Similarly, to find the odds against selecting a vowel, we will consider the number of unfavorable outcomes (not selecting a vowel) and divide it by the total number of outcomes.

Let's start by finding the number of vowels and consonants in the word ARITHMETIC:

Vowels: A, I, E, I (total of 4 vowels)
Consonants: R, T, H, M, T, C (total of 6 consonants)

Total letters in the word: 4 vowels + 6 consonants = 10 letters

To calculate the odds in favor of selecting a vowel, we divide the number of favorable outcomes (4 vowels) by the total number of outcomes (10 letters):

Odds in favor of selecting a vowel = 4/10 = 2/5

To express this as a ratio, we can say that the odds in favor of selecting a vowel are 2 to 5.

Now, for the odds against selecting a vowel, we divide the number of unfavorable outcomes (6 consonants) by the total number of outcomes (10 letters):

Odds against selecting a vowel = 6/10 = 3/5

Expressed as a ratio, the odds against selecting a vowel are 3 to 5.

how do i write this into an expression? 1/3 of a number