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

If four coins are flipped, find the probability of obtaining two heads and two tails.
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.
A group of six students is chosen at random from a list of five maths students and four psychology students. What is the probability that four maths students and two psychology students are chosen?
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?
A group of five students went to a hotel with 10 upper floors and a ground floor. The students simultaneously enter the elevator at the ground floor. The students choose their exit floors independently of each other. Determine the probability that they are all going to different floors when each student randomly chooses one of the 10 floors as their exit floor.
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 )
There are 3 bags. The first bag contains 3 red and 7 black balls. The second bag contains 8 red and 2 black balls. The third bag contains 4 red and 6 black balls. One bag is selected randomly and a ball is drawn from it. If the drawn ball is red, the probability that it was drawn from the third bag is
A teacher will pick 1 student at random from 20 for the lead in a play. What is the probability of a student, Jo, of winning?
In a suitcase there are 5 orange, y green, (y+2) grey and 6 yellow pens. Probability of choosing one green pen from the given suitcase is 1/3. What is the sum of the number of green, grey and yellow pens?
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.
A student has a total of 10 books and 3 of her books are science fiction. If she arranges them on a shelf randomly, what is the probability that the 3 science fiction books are all together?