An AIMS student walked into a room where he found N pieces of wire. After finding the 2V 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?

An AIMS student walked into a room where he found N pieces of wire. After finding the 2V 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...

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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?

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