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

2/5 abd 3/5?

a vowel is a,e,i,o,u so count how many letters there are in the word then count how many a,e,i,o,u, letters there there are then put the number of vowels there are over the amount of letters there are in the word then simplifiy

4/10

yes

or 2/5

To calculate the odds in favor of selecting a vowel from the word ARITHMETIC, we need to determine the number of favorable outcomes (vowels) and the number of possible outcomes (total letters).

Step 1: Count the number of vowels in the word ARITHMETIC.
The vowels in ARITHMETIC are A, I, and E. There are 3 vowels.

Step 2: Count the number of total letters in the word ARITHMETIC.
The word ARITHMETIC has 9 letters.

Step 3: Calculate the odds in favor of selecting a vowel.
The odds in favor of selecting a vowel are expressed as the probability of selecting a vowel divided by the probability of not selecting a vowel.

Probability of selecting a vowel = Number of vowels / Number of total letters
Probability of selecting a vowel = 3 / 9
Probability of selecting a vowel = 1/3

Probability of not selecting a vowel = 1 - Probability of selecting a vowel
Probability of not selecting a vowel = 1 - 1/3
Probability of not selecting a vowel = 2/3

Odds in favor of selecting a vowel = Probability of selecting a vowel / Probability of not selecting a vowel
Odds in favor of selecting a vowel = (1/3) / (2/3)
Odds in favor of selecting a vowel = 1/2

Therefore, the odds in favor of selecting a vowel are 1/2 or 2/4.

To find the odds against selecting a vowel, we subtract the odds in favor of selecting a vowel from the total odds.

Total odds = 1 (in favor) + 1 (against)
Total odds = 2

Odds against selecting a vowel = Total odds - Odds in favor of selecting a vowel
Odds against selecting a vowel = 2 - 1 (in favor)
Odds against selecting a vowel = 1

Therefore, the odds against selecting a vowel are 1 or 1/1.