Solution Found!
Answer: A computer system uses passwords that contain
Chapter 2, Problem 120E(choose chapter or problem)
Problem 120E
A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let ? denote the set of all possible passwords. Suppose that all passwords in ? are equally likely. Determine the probability for each of the following:
(a) Password contains all lowercase letters given that it contains only letters
(b) Password contains at least 1 uppercase letter given that it contains only letters
(c) Password contains only even numbers given that is contains all numbers
Questions & Answers
QUESTION:
Problem 120E
A computer system uses passwords that contain exactly eight characters, and each character is one of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let ? denote the set of all possible passwords. Suppose that all passwords in ? are equally likely. Determine the probability for each of the following:
(a) Password contains all lowercase letters given that it contains only letters
(b) Password contains at least 1 uppercase letter given that it contains only letters
(c) Password contains only even numbers given that is contains all numbers
ANSWER:
Solution:
Step 1 of 4:
Given that, a computer system uses passwords that contain exactly eight characters.
Let A be the passwords with all letters.
B be the passwords with all 26 lowercase letters (a-z).
C be the passwords with at least 1 uppercase letter (A-Z).
We have to determine the probability for each of the following: