Problem 8. Suppose I have 50 strings. At every step, I randomly pick 2 ends of strings (they could be the ends of the same string) and tie them together. At each step, I could make either a longer string or a loop. a) What is the expected number of steps it takes me to turn all the strings into loops? b) What is the expected number of loops? (Express this as a sum)

Problem 8. Suppose I have 50 strings. At every step, I randomly pick 2 ends of strings (they could be the ends of the same string) and tie them together. At each step, I could make either a longer string or a loop. a) What is the expected number of steps it takes me to turn all the strings into loops? b) What is the expected number of loops? (Express this as a sum)

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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Problem 8. Suppose I have 50 strings. At every step, I randomly pick 2 ends of strings
(they could be the ends of the same string) and tie them together. At each step, I could
make either a longer string or a loop.
a) What is the expected number of steps it takes me to turn all the strings into loops?
b) What is the expected number of loops? (Express this as a sum)

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