# A probability problem

Jump to navigation
Jump to search

A Dartmouth student asked his math teacher Dana Williams if he could solve the following problem:

QUESTION: We start with n ropes and gather their 2n ends together.

Then we randomly pair the ends and make n joins. Let E(n)

be the expected number of loops. What is E(n)?

You might be interested in trying to solve this problem. You can check your answer here.