The digit 1, 2, ..., n(n > 5) are put at random in a row. (a)...
The digit 1, 2, ..., n(n > 5) are put at random in a row.
(a) Show that the probability that the digits 4 and 5 will be adjacent is 2/n.
(b) Find the probability that the digits 4 and 5 will not be adjacent.
(c) Find the probability that the digits 4 and 5 will be adjacent or the digits 2 and 3 will be adjacent. That is, find P((4 and 5 adjacent) ∪ (2 and 3 adjacent)).
Homework Answers
A lottery ticket costs $2 and has a random 5-digit number. The payoff depends on the...
A lottery ticket costs $2 and has a random 5-digit number. The payoff depends on the largest number of repeated digits. There is no prize if no digit is repeated. The prize is $2 if some digit is repeated exactly twice, $5 if a digit is repeated exactly 3 times, $10 if a digit is repeated exactly 4 times, and $1000 if a digit is repeated exactly 5 times. Let X be the net earning in playing the game. a)...
a.) Suppose that n people are seated in a random manner in a row of n...
a.) Suppose that n people are seated in a random manner in a row of n theater seats. What is the probability that two particular people A and B will be seated next to each other? The answer to the question is 2/n, but I'm not sure how to do the process. My teacher said that it was the # of favorable outcomes/ total number of outcomes, which was 2* (n-1)! / n!, which simplifies to 2/n. Is this process...
A large collection of one-digit random numbers should have about 50% odd and 50% even digits...
A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8) a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 9 0 49 0 5 0 7 8 1 7 8 3 4 5 0 7 1 5 7 5 1 2...
2: Exercise 1.24. There are n married couples arranged at random in a row. 1. Find...
2: Exercise 1.24. There are n married couples arranged at random in a row. 1. Find the probability that no husband sits next to his wife. 2. Compute this probability explicitly when n 3.
Consider the experiment of picking a four-digit PIN uniformly at random over all possible four-digit PINs,...
Consider the experiment of picking a four-digit PIN uniformly at random over all possible four-digit PINs, and define the random variables: X = number of distinct digits (i.e. how many different digits appear once or more) Y = length of longest streak of the same digit Below are the values of the random variables for some sample outcomes: X(1,3,1, 3)) = 2, Y((1,3,1,3)) = 1, X(2, 4, 3, 3)) = 3, Y(2, 4, 3, 3)) = 2, X (2,2, 4,...
Use row-reduction to put the following matrix to reduced row echelon form. 1 5 4 2...
Use row-reduction to put the following matrix to reduced row echelon form. 1 5 4 2 1 2 0 0 3 0 Show each step.
Question 3 Use row-reduction to put the following matrix to reduced row echelon form. 5 1...
Question 3 Use row-reduction to put the following matrix to reduced row echelon form. 5 1 1 7 4 2 1 2 0 0 3 0 Show each step.
2) (5pts) A 3-digit number will be formed using the digits 1, 2, 3, 4, 5;...
2) (5pts) A 3-digit number will be formed using the digits 1, 2, 3, 4, 5; using each digit only once. a) How many possible 3-digit numbers are possible? TOTAL: b) Assume three of the digits are randomly chosen and randomly permuted in order to form the 3-digit number. Then each of the possible 3-digit numbers in part a) are equally likely. Find the probability that the 3-digit number ends up being an even number greater than or equal to...
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7,...
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 194 allegedly fraudulent checks written to a bogus company by an employee attempting to...
Question 4 of 5 (1 point) 11.5 Secuuri elercise 1 A four-digit identification card is made....
Question 4 of 5 (1 point) 11.5 Secuuri elercise 1 A four-digit identification card is made. Find the probability that the card will contain the digits 0, 1, 2, 3 in any order. (Round your answer to five decimal places.) The probability that the card will contain the digits 0, 1, 2, 3 in any order is
A large collection of one-digit random numbers should have about 50% odd and 50% even digits because five of the ten digits are odd (1, 3, 5, 7, and 9) and five are even (0, 2, 4, 6, and 8) a. Find the proportion of odd-numbered digits in the following lines from a random number table. Count carefully. 9 0 49 0 5 0 7 8 1 7 8 3 4 5 0 7 1 5 7 5 1 2...
2: Exercise 1.24. There are n married couples arranged at random in a row. 1. Find the probability that no husband sits next to his wife. 2. Compute this probability explicitly when n 3.
Consider the experiment of picking a four-digit PIN uniformly at random over all possible four-digit PINs, and define the random variables: X = number of distinct digits (i.e. how many different digits appear once or more) Y = length of longest streak of the same digit Below are the values of the random variables for some sample outcomes: X(1,3,1, 3)) = 2, Y((1,3,1,3)) = 1, X(2, 4, 3, 3)) = 3, Y(2, 4, 3, 3)) = 2, X (2,2, 4,...
Use row-reduction to put the following matrix to reduced row echelon form. 1 5 4 2 1 2 0 0 3 0 Show each step.
Question 3 Use row-reduction to put the following matrix to reduced row echelon form. 5 1 1 7 4 2 1 2 0 0 3 0 Show each step.
2) (5pts) A 3-digit number will be formed using the digits 1, 2, 3, 4, 5; using each digit only once. a) How many possible 3-digit numbers are possible? TOTAL: b) Assume three of the digits are randomly chosen and randomly permuted in order to form the 3-digit number. Then each of the possible 3-digit numbers in part a) are equally likely. Find the probability that the 3-digit number ends up being an even number greater than or equal to...
The first significant digit in any number must be 1, 2, 3, 4, 5, 6, 7, 8, or 9. It was discovered that first digits do not occur with equal frequency. Probabilities of occurrence to the first digit in a number are shown in the accompanying table. The probability distribution is now known as Benford's Law. For example, the following distribution represents the first digits in 194 allegedly fraudulent checks written to a bogus company by an employee attempting to...
Question 4 of 5 (1 point) 11.5 Secuuri elercise 1 A four-digit identification card is made. Find the probability that the card will contain the digits 0, 1, 2, 3 in any order. (Round your answer to five decimal places.) The probability that the card will contain the digits 0, 1, 2, 3 in any order is
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