Question

4 letters are typed, without repetition. What is the probability that all 4 will be vowels? Write your answer asa percent. Round your answer to three decimal places.The probability is

Answer 1

There are 26 letters in the alphabet, 5 are vowels, therefore, the probability of choosing a vowel the first time is:

$\frac{5}{26},$

and the second time is:

$\frac{4}{25}\text{.}$

Continuing with this reasoning, we get that the probabilities each time are:

$\frac{5}{26},\frac{4}{25},\frac{3}{24},\frac{2}{23}\text{.}$

Finally, the probability that you get all vowels is the product of the probabilities:

$\frac{1}{2990}\text{.}$

Writing the above result as a percentage we get:

$0.033\%.$

Answer:

$0.033\%\text{.}$