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:

`(5)/(26),`

and the second time is:

`(4)/(25)\text{.}`

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

`(5)/(26),(4)/(25),(3)/(24),(2)/(23)\text{.}`

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

`(1)/(2990)\text{.}`

Writing the above result as a percentage we get:

`0.033\%.`

Answer:

`0.033\%\text{.}`