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) :-
[tex](26)^5=11881376[/tex]
(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) :-
[tex](21)^5=4084101[/tex]
Now, the probability that the random string contains no vowels (A, E, I, O, U) will be :_
[tex]\dfrac{\text{Number of strings made without vowel}}{\text{Total number of strings}}\\\\=\dfrac{4084101}{11881376}\\\\=0.343739731829\approx0.3437[/tex]
