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A computer system uses passwords that are exactly seven
Chapter 2, Problem 110E(choose chapter or problem)
Problem 110E
A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). You maintain a password for this computer system. Let A denote the subset of passwords that begin with a vowel (either a, e, i, o, or u) and let B denote the subset of passwords that end with an even number (either 0, 2, 4, 6, or 8).
(a) Suppose a hacker selects a password at random. What is the probability that your password is selected?
(b) Suppose a hacker knows that your password is in event A and selects a password at random from this subset. What is the probability that your password is selected?
(c) Suppose a hacker knows that your password is in A and B and selects a password at random from this subset. What is the probability that your password is selected?
Questions & Answers
QUESTION:
Problem 110E
A computer system uses passwords that are exactly seven characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). You maintain a password for this computer system. Let A denote the subset of passwords that begin with a vowel (either a, e, i, o, or u) and let B denote the subset of passwords that end with an even number (either 0, 2, 4, 6, or 8).
(a) Suppose a hacker selects a password at random. What is the probability that your password is selected?
(b) Suppose a hacker knows that your password is in event A and selects a password at random from this subset. What is the probability that your password is selected?
(c) Suppose a hacker knows that your password is in A and B and selects a password at random from this subset. What is the probability that your password is selected?
ANSWER:
Solution
Step 1 of 4
Given that the computer password having 7 characters
Let A is the event that the password starts with vowel
Let B is the event that the password ends with even number
The no.of characters =26 letters+10 digits
=36
The no.of ways of arranging the password=(36)7