Question

A computer generates a random five-digit string in the symbols A, B, C, ..., Z. (a) How many such strings are possible? (b) What is the probability that the random string contains no vowels (A, E, I, O, U)? (Round your answer to four decimal places.)

Answer 1

Answer:  (a)  11881376

(b) 0.3437

Step-by-step explanation:

Given : A computer generates a random five-digit string in the symbols A, B, C, ..., Z.

Total number of letters in English Alphabet= 26

(a) If computer generates a random five-digit string , then the total number of such strings are possible (if repetition is allowed) :-

$(26)^5=11881376$

(b) If we do not include all the vowels  (A, E, I, O, U) = 26-5=21

If computer generates a random five-digit string , then the random string contains no vowels (A, E, I, O, U) (if repetition is allowed) :-

$(21)^5=4084101$

Now, the probability that the random string contains no vowels (A, E, I, O, U) will be :_

$\dfrac{\text{Number of strings made without vowel}}{\text{Total number of strings}}\\\\=\dfrac{4084101}{11881376}\\\\=0.343739731829\approx0.3437$