There are 26 letters in the alphabet, 5 are vowels, therefore, the probability of choosing a vowel the first time is:
[tex]\frac{5}{26},[/tex]and the second time is:
[tex]\frac{4}{25}\text{.}[/tex]Continuing with this reasoning, we get that the probabilities each time are:
[tex]\frac{5}{26},\frac{4}{25},\frac{3}{24},\frac{2}{23}\text{.}[/tex]Finally, the probability that you get all vowels is the product of the probabilities:
[tex]\frac{1}{2990}\text{.}[/tex]Writing the above result as a percentage we get:
[tex]0.033\%.[/tex]Answer:
[tex]0.033\%\text{.}[/tex]