Question

In: Statistics and Probability

Given a security code for door access consists of 4 alphanumeric characters, and the first character...

Given a security code for door access consists of 4 alphanumeric characters, and the first character has to be a letter. Determine the proportion of security code that:
1. is a unique code
2. begin with a vowel (a, e, i, o, u)
3. end with odd number (1, 3, 5, 7, 9)
4. begin with a vowel and end with odd number

Solutions

Expert Solution

a. Proportion of security code that: is a unique code

Security code :

First character has to be a letter : Number of possibilities : 26(Case not considered)

Second character : Alphanumeric : Number of possibilities : 26(letters) + 10 numeric digits = 36

Third character : Alphanumeric : Number of possibilities : 26(letters) +10 numeric digits = 36

Fourth character: Alphanumeric : Number of possibilities : 26(letters) + 10 numeric digits = 36

Total number of possibilities = 26 x 36 x 36 x 36 = 1213056

Unique code : 1

Proportion of security code that: is a unique code = 1/1213056

b. begin with a vowel (a, e, i, o, u)

First character has to be a vowel (a,e,i,o,u) : Number of possibilities :5(Case not considered)

Second character : Alphanumeric : Number of possibilities : 26(letters) + 10 numeric digits = 36

Third character : Alphanumeric : Number of possibilities : 26(letters) + 10 numeric digits = 36

Fourth character: Alphanumeric : Number of possibilities : 26(letters) + 10 numeric digits = 36

Total number of possible security codes that begin with a vowel (a, e, i, o, u) = 5*36*36*36 = 233280

Total number of possibilities = 1213056

Proportion of security code that begin with a vowel (a, e, i, o, u)= 233280/1213056 = 0.1923

c. end with odd number (1,3,5,7,9)

First character has to be a letter Number of possibilities :26(Case not considered)

Second character : Alphanumeric : Number of possibilities : 26(letters) +10 numeric digits = 36

Third character : Alphanumeric : Number of possibilities : 26(letters) +10 numeric digits = 36

Fourth character: odd number (1,3,5,7,9) : Number of possibilities : 5

Total number of possible security codes that end with odd number (1,3,5,7,9) = 26*36*36*5 = 168480

Total number of possibilities = 1213056

Proportion of security code end with odd number (1,3,5,7,9) = 168480/1213056 = 0.1389

d. begin with a vowel and end with odd number

First character has to be a vowel (a,e,i,o,u) : Number of possibilities :5(Case not considered)

Second character : Alphanumeric : Number of possibilities : 26(letters) +10 numeric digits = 36

Third character : Alphanumeric : Number of possibilities : 26(letters) +10 numeric digits = 36

Fourth character: odd number (1,3,5,7,9) : Number of possibilities : 5

Total number of possible security codes begin with a vowel and end with odd number = 5 * 36 * 36 * 5 = 32400

Total number of possibilities = 1213056

Proportion of security code begin with a vowel and end with odd number= 32400/1213056 = 0.0267

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Your I-phone has a numeric passcode to press to access it. This code consists of 4...

Your I-phone has a numeric passcode to press to access it. This code consists of 4 numbers. If someone tries the codes and gets them incorrect, the phone will shut down after three incorrect attempts. What is the probability that a person who is just guessing the code will get it correct within three guesses (hint…how does this compare to the probability of not getting it right in three attempts)?

Suppose that the security code for a particular automobile’s locks consists of 4 bytes of data...

Suppose that the security code for a particular automobile’s locks consists of 4 bytes of data transmitted via a low power radio. A byte is either sent correctly or is distorted by interference. The car locks are only opened if all 4 bytes are received correctly. Let C be the event that a byte is received correctly and F be the event that the byte is distorted in transmission. Then CCCC would mean that all four bytes were received correctly...

Write a java code that first discards as many whitespace characters as necessary until the first...

Write a java code that first discards as many whitespace characters as necessary until the first non-whitespace character is found. Then, starting from this character, takes an optional initial plus or minus sign followed by as many numerical digits as possible, and interprets them as a numerical value. The string can contain additional characters after those that form the integral number, which are ignored and have no effect on the behavior of this function. If the first sequence of non-whitespace...

the curb weight of a 4-door sedan vehicle is given as 1050kg for unladen conditions. if...

the curb weight of a 4-door sedan vehicle is given as 1050kg for unladen conditions. if the weight on the front axle is 60 kg and wheelbase is 2.75m, calculate the fore/aft position of the center of gravity. if this vehicle starts to accelerate with 2m/s^2 from zero initial speed on a 6% grade road (moving uphill), calculate the load distribution on the axles. assume that the height of the center of gravity is 0.5m

Using python: Given a string x, write a program to check if its first character is...

Using python: Given a string x, write a program to check if its first character is the same as its last character. If yes, the code should output "True"

Computer Security Bell-LaPadula Model Given the access rights as follows: Nada can read and write to...

Computer Security Bell-LaPadula Model Given the access rights as follows: Nada can read and write to file A, can append to file B, and can write to file C. Maha can read file A, can write to file B, and cannot access file C. Write the access control matrix M that specifies the described set of access rights for subjects Nada and Maha to objects file A, file B and file C. Then the subject’s security levels are LNada= Confidential...

The code file is attached. Portion of the code is given (1, 2, 3, 4). You...

The code file is attached. Portion of the code is given (1, 2, 3, 4). You have to write the code for the remaining items (5, 6, 7). #include <iostream> using namespace std; struct node { int data; node* next; }; node* head=NULL; void appendNode(int value) { node *newNode, *curr; newNode = new node(); newNode->data=value; newNode->next=NULL; if (!head) head=newNode; else { curr=head; while (curr->next) curr = curr->next; curr->next = newNode; } } void insertNode(int value) { node *newNode, *curr, *previous;...

Was there discrimination on the Titanic? Were first-class passengers given greater access to life boats? The...

Was there discrimination on the Titanic? Were first-class passengers given greater access to life boats? The unsinkable liner Titanic collided with an iceberg on her maiden voyage in 1912 and sank with great loss of life. On board were 1317 passengers, some of whom had paid a very much higher fare than others for the voyage. A not very subtle sub-text in the most recent Titanic movie was the notion that the first class passengers survived at a higher rate...

4. Given the following code for AES Electronic Code Block implementation for the encryption functionality. Modify...

4. Given the following code for AES Electronic Code Block implementation for the encryption functionality. Modify the code to create a function named ‘decryptECB(key, ciphertext)’ that accepts key and ciphertext and returns a plaintext. from base64 import b64decode from Crypto.Cipher import AES from Crypto.Util.Padding import pad from Crypto.Util.Padding import unpad # We assume that the password was securely shared beforehand password = input ("Enter the password to decrypt the message: ") key= pad(password.encode(), 16) ciphertext = input ("Paste the cipher...

[Hash Tables] Given the following code in C++, implement the functions in table2.cpp. The first 2...

[Hash Tables] Given the following code in C++, implement the functions in table2.cpp. The first 2 files (table2.h, short story text file) are all fully coded and commented for convenience. *****I have given references that I've completed previously for the table2.cpp file, I just need help applying them. Will provide good rating, thanks****** -------------------------------------------------------------------------------------------------------------------------- table2.h (given file, do not edit): // FILE: table2.h // // ABSTRACT BASE CLASS: Table // 1. The number of records in the Table is...

Subjects