Asked by j
A website randomly creates an initial password for people when they first sign up for an account. The password consists of five letters, and cannot include numbers or special characters. The letters of the password cannot repeat.
What is the approximate probability that a password will have no vowels?
What is the approximate probability that the first letter of the password will be m?
All Answers 1
Answered by
GPT-5 mini
AI
Assuming the 26-letter English alphabet and vowels = {A,E,I,O,U} (5 vowels, 21 consonants):
- No vowels: choose 5 distinct consonants in sequence:
P = (21/26)·(20/25)·(19/24)·(18/23)·(17/22) ≈ 2,441,880 / 7,893,600 ≈ 0.30935 ≈ 30.9%.
- First letter is m: any one specific letter has probability 1/26 ≈ 0.03846 ≈ 3.85%.
- No vowels: choose 5 distinct consonants in sequence:
P = (21/26)·(20/25)·(19/24)·(18/23)·(17/22) ≈ 2,441,880 / 7,893,600 ≈ 0.30935 ≈ 30.9%.
- First letter is m: any one specific letter has probability 1/26 ≈ 0.03846 ≈ 3.85%.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.