A computer system uses passwords that contain exactly six characters, and each character is 1 of...

A computer system uses passwords that contain exactly six characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the number of passwords in each of the following events.

(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 it contains all numbers

Expert Solution

milcah answered 5 months ago

A computer system uses passwords that contain exactly 5 characters, and each character is 1 of...

A computer system uses passwords that contain exactly 5 characters, and each character is 1 of the 3 lowercase letters (a, b, c) or 3 upper case letters (A, B, C) or the 5 odd digits (1, 3, 5, 7, 9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with only letters or only integers, respectively. Determine the probability that a password contains at least 1 uppercase...

A password is a sequence of five characters. Each character is one of twenty-six uppercase letters...

A password is a sequence of five characters. Each character is one of twenty-six uppercase letters (“A” through “Z”), one of ten digits (“0” through “9”), or one of five symbols (“+”, “-”, “!”, “<”, “>”). Count the number of possible passwords that can be created in each of the following scenarios. Consider each part of this questions separately. (a) There are no restrictions on how the characters are chosen. (b) A password must begin with a letter and end...

Passwords on an ancient computer are required to be 4-5 characters long and made up of...

Passwords on an ancient computer are required to be 4-5 characters long and made up of lower case letters only (a..z : there are 26 possibilities). Please answer each of these questions below, giving numerical answers. You should also explain how you got each answer, for full or partial credit. a) Assume that letters may NOT be repeated, and passwords are 4-5 letters long. How many passwords are possible? b) Assume that letters MAY be repeated, and passwords are 4-5...

A password is a string of ten characters, where each character is a lowercase letter, a...

A password is a string of ten characters, where each character is a lowercase letter, a digit, or one of the eight special characters !, @, #, $, %, &, (, and ). A password is called awesome, if it contains at least one digit or at least one special character. Determine the number of awesome passwords.

For this question, a block is a sequence of 20 characters, where each character is one...

For this question, a block is a sequence of 20 characters, where each character is one of the 26 lowercase letters a-z. For example, these are blocks: iwpiybhunrplsovrowyt rpulxfsqrixjhrtjmcrr fxfpwdhwgxtdaqtmxmlf How many different blocks are there? A block is squarefree if no character appears two times consecutively. The first and third example above are squarefree, but the second example is not because of the two consecutive occurrences of r. How many squarefree blocks are there? A block is non-local if...

Find the number of passwords that use each of the digits 3,4,5,6,7,8,9 exactly once. IN how...

Find the number of passwords that use each of the digits 3,4,5,6,7,8,9 exactly once. IN how many of the passwords: 1. are the four odd digits consecutive? 2. are no two odd digits consecutive? 3. are the first three digits even? 4. are the three even digits consecutive?

A database uses 20-character strings as record identifiers. The valid characters in these strings are upper-case...

A database uses 20-character strings as record identifiers. The valid characters in these strings are upper-case letters in the English alphabet and decimal digits. (Recall there are 26 letters in the English alphabet and 10 decimal digits.) How many valid record identifiers are possible if a valid record identifier must meet all of the following criteria: Letter(s) from the set {A,E,I,O,U} occur in exactly three positions of the string. The last three characters in the string are distinct decimal digits...

JAVA MASTERMIND The computer will randomly select a four-character mastercode. Each character represents the first letter...

JAVA MASTERMIND The computer will randomly select a four-character mastercode. Each character represents the first letter of a color from the valid color set. Our valid color choices will be: (R)ed, (G)reen, (B)lue and (Y)ellow. Any four-character combination from the valid color set could become the mastercode. For example, a valid mastercode might be: RGBB or YYYR. The game begins with the computer randomly selecting a mastercode. The user is then given up to 6 tries to guess the mastercode....

A hacker has programmed their computer to generate, uniformly at random, an eight-character password, with each...

A hacker has programmed their computer to generate, uniformly at random, an eight-character password, with each character being either one of 26 lower-case letters (a-z), one of 26 upper-case letters (A-Z) or one of 10 integers (0-9). The hacker wants to infiltrate a website that has 2 million users. Assume, for simplicity, that each user is required to use a unique password. What is the expected number of attempts before the hacker successfully generates a user password? What is the...

1. consider the followi axiomatic system: A1: Each bot pats exactly 2 tobs. A2: For each...

1. consider the followi axiomatic system: A1: Each bot pats exactly 2 tobs. A2: For each pair of distinct tobs, there is a bot that pats both tobs. A3: There are exactly 5 tobs. (a) Pick one of the three axioms and prove that it is independent from the other axioms in the system. Be sure to justify your answer. (b) Find the minimum number of bots present in a model for this system. Be sure to justify your...

Question