3 letters are typed, without repetition. What is the probability that all 3 will be vowels? Write your answer as a percent. Round your answer to three decimal places.
To find the probability that all three letters will be vowels, we first need to determine the total number of possible outcomes.
There are 26 letters in the English alphabet, and since we are not allowing repetition, the first letter can be any vowel (A, E, I, O, or U), leaving us with 5 options.
For the second letter, since repetition is not allowed, there are only 4 vowel options left.
Finally, for the third letter, there are 3 vowel options left.
So, the total number of possible outcomes is (5 options for the first letter) * (4 options for the second letter) * (3 options for the third letter) = 60 possible outcomes.
Now, let's determine the number of favorable outcomes, i.e., the number of outcomes where all three letters are vowels.
Since repetition is not allowed, the first letter can still be any vowel (5 options).
For the second letter, there are 4 vowel options left.
Finally, for the third letter, there are 3 vowel options left.
So, the number of favorable outcomes is (5 options for the first letter) * (4 options for the second letter) * (3 options for the third letter) = 60 favorable outcomes.
To find the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability = (Number of Favorable Outcomes) / (Total Number of Possible Outcomes) = 60 / 60 = 1
Finally, to express the probability as a percentage, we multiply by 100:
Probability as a percent = 1 * 100 = 100%
Therefore, the probability that all three letters will be vowels is 100%.
To calculate the probability of all 3 letters being vowels, we need to know the total number of possibilities and the number of possibilities in which all 3 letters are vowels.
Let's start by determining the total number of possibilities.
Since we are typing 3 letters without repetition, we have 26 options for the first letter, 25 options for the second letter (since 1 letter has already been used), and 24 options for the third letter. Therefore, the total number of possibilities is:
26 * 25 * 24 = 15,600
Next, let's determine the number of possibilities in which all 3 letters are vowels.
Out of the 26 letters in the alphabet, there are 5 vowels (a, e, i, o, u). Since we are typing 3 letters without repetition, there are 5 options for the first vowel, 4 options for the second vowel (since 1 vowel has already been used), and 3 options for the third vowel. Therefore, the number of possibilities in which all 3 letters are vowels is:
5 * 4 * 3 = 60
Finally, let's calculate the probability by dividing the number of favorable outcomes (all 3 vowels) by the total number of possibilities and converting it to a percentage:
(60 / 15,600) * 100 = 0.385%
Rounded to three decimal places, the probability that all 3 letters will be vowels is 0.385%.