A student walked into a room where he found N pieces of wire. After finding the 2N ends, he casually joined these ends together in pairs until there were no loose ends left. In every turn, he selected one of the unjoined ends with equal probability, and then another unjoined end with equal probability, and then tied the two ends together. Another student found the pile of loops and decided to count how many there are. She reasons that there could be anything from one long loop to N separate loops. What is the expected number of loops if there were five wires in the room?

A student walked into a room where he found N pieces of wire. After finding the 2N ends, he casually joined these ends together in pairs until there were no loose ends left. In every turn, he selected one of the unjoined ends with equal probability, and then another unjoined end with equal probability, and then tied the two ends together. Another student found the pile of loops and decided to count how many there are. She reasons that there could be anything from one long loop to N separate loops. What is the expected number of loops if there were five wires in the room?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

In a bag there are 7 blue, 3 yellow, and 4 pink markers. If five markers are selected at random and the color noted, find the probability that none are yellow given that none are pink.
In a box there are 3 red, 4 blue, and 5 white marbles. If 3 marbles are selected at random and the colors are noted, find the probability that all are white given that all are the same color.
The mathematics department of a college has 8 male professors, 11 female professors, 14 male teaching assistants, and 7 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a professor or a female.
If one of the 1156 people is randomly selected, find the probability that the person is a man or a heavy smoker. 770 men and 7 heavy smoker so 777 total out of the 1156 people
Suppose you have created a new playlist made up of 6 songs (2 rock, 2 hip-hop, and 2 trance). Find the probability that if the iPod is on shuffle, the first song played will be hip-hop and the second played will be trance. Your answer should be in fraction form.
A ball is chosen at random out of a bowl that contains 3 red balls, 2 green balls, and 1 blue ball, and then a selection is made from the remaining 5 balls. Find the probability that a red ball and a green ball are selected.
Pablo randomly picks five marbles from a bag of eleven marbles (six red ones, three green ones, and two yellow ones). How many outcomes are there in the event that all of the marbles he picks are red?
Bonnie and Connie are twins with identical purses. Bonnie needs 35 cents to pay for a parking meter. Suppose that Bonnie's purse has 5 quarters, 3 dimes, and 2 nickels while Connie's purse has 2 quarters, 5 dimes, and 3 nickels in it. Not being able to tell the difference between the purses, Connie picks one at random and grabs two coins from it. What is the probability that Bonnie picked her own purse given that she drew out enough change to pay for her parking meter? (Note: Bonnie needs to put in at least 35 cents to pay her parking meter.)
A lock consists of 3 dials, where each dial has 4 letters. What is the probability of guessing the right combination in one try? Kay has an 80% probability of making a free-throw in basketball, and each free-throw is independent. Kay gets to take 2 free-throws and must make both to win the game. What is the probability that Kay's team will win the game? Two owners of a cattle ranch, Jo and Val, want to find the average weight for the ranch’s 200 cows. Instead of weighing all of the cows: Jo weighs 25 cows and gets an average weight of 1,350 pounds (stdev 50) Val weighs 100 cows and gets an average weight of 1,420 pounds (stdev 50) What is Jo’s margin of error, rounded to the nearest whole number? (The formula is )
The mathematics department of a college has 6 male professors, 11 female professors, 10 male teaching assistants, and 12 female teaching assistants. If a person is selected at random from the group, find the probability that the selected person is a teaching assistant or a female.
Suppose 4 letters from a sign reading "Montreal" fell on the street. A mathematician find the 4 letters and randomly place them back on the sign (each of them on a spot where a letter fell off). What is the probability the sign reads "Montreal"?
At bedtime, you read three books to your kids, Walker, Michael, and Luke. Together, they have 3232 books. If you decide to randomly choose three books, what is the probability that the three you choose will consist of each of their favorite books? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.