Question

5 letters are typed, with repetition allowed. What is the probability that all 5 will be vowels? Write your answer as apercent. Round to the nearest hundredth of a percent as needed.The probability is%.Check Answer

Answer 1

The probability is given by :

`P=(Event)/(TotalEvents)`

Note that there are 5 vowels in the English Alphabet with 26 total letters and repetition is allowed.

So the event of selecting all vowels is :

Event = 5 x 5 x 5 x 5 x 5 = 5^5

Total Events = 26 x 26 x 26 x 26 x 26 = 26^5

The probability will be :

`p=(5^5)/(26^5)`
`p=0.000263=0.03\%`