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A computer system uses passwords that are exactly six
Chapter 3, Problem 107E(choose chapter or problem)
Problem 107E
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) one billion passwords from the potential set, and a match to a user’s password is called a hit.
(a) What is the distribution of the number of hits?
(b) What is the probability of no hits?
(c) What are the mean and variance of the number of hits?
Questions & Answers
QUESTION:
Problem 107E
A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) one billion passwords from the potential set, and a match to a user’s password is called a hit.
(a) What is the distribution of the number of hits?
(b) What is the probability of no hits?
(c) What are the mean and variance of the number of hits?
ANSWER:
Solution:
Step 1 of 4:
The total characters of password = 26 (letters) + 10 (integers)
= 36.
The possible number of six digit password is .
Total users = 10,000