3 letters are typed, with repetition allowed. What is the probability that all 3 will be vowels? Write your answer as a percent. Round to the nearest hundredth of a percent as needed.

of the 26 letters, 5 are vowels

prob (3 vowels of 3)
= (5/26)(5/26)(5/26)
= appr .0071
or .01 to the nearest hundredth

.0071 converted to a percentage (multiply by 100) is 0.71 % to the nearest 100th percent.

Well, let's see here. We have 26 letters in the English alphabet, and out of those, 5 are vowels (a, e, i, o, u). Since repetition is allowed, we have the possibility of choosing any of those 5 vowels for each of the 3 letters. So, the probability of each letter being a vowel is 5/26. To find the probability of all 3 letters being vowels, we need to multiply these probabilities together: (5/26) * (5/26) * (5/26) = 125/17576. Now, to express this as a percentage, we need to multiply this fraction by 100: (125/17576) * 100 = 0.7103%. So, the probability is approximately 0.71%.

To find the probability that all 3 letters typed will be vowels, we need to know the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since repetition is allowed and there are 26 letters in the English alphabet, we have 26 choices for each of the 3 letters. Therefore, the total number of possible outcomes is 26*26*26 = 26^3 = 17576.

Now, let's determine the number of favorable outcomes. There are 5 vowels in the English alphabet: A, E, I, O, and U. Since repetition is allowed, we have 5 choices for each of the 3 letters. Therefore, the number of favorable outcomes is 5*5*5 = 5^3 = 125.

To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes: 125/17576 ≈ 0.00711.

To express this as a percent, we multiply by 100: 0.00711 * 100 ≈ 0.71%.

Therefore, the probability that all 3 letters typed will be vowels is approximately 0.71%.

To calculate the probability that all 3 letters will be vowels, we need to know the total number of possible outcomes and the number of favorable outcomes.

First, let's determine the total number of possible outcomes. Since repetition is allowed and there are no restrictions on the letters, there are 26 options for each letter (26 letters in the alphabet).

Therefore, the total number of possible outcomes is 26 * 26 * 26 = 17,576.

Now, let's determine the number of favorable outcomes. In this case, we only want vowels, which are the letters A, E, I, O, and U. There are 5 vowels in total.

Since we are allowed repetition, for each letter, there are 5 options (the vowels). So the number of favorable outcomes is 5 * 5 * 5 = 125.

Now we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes)
Probability = 125 / 17,576

To write this as a percent, we need to multiply the probability by 100 and round to the nearest hundredth of a percent.

Probability = (125 / 17,576) * 100 ≈ 0.71%

Therefore, the probability that all 3 letters typed will be vowels is approximately 0.71%.