MAA MathFest, Madison, WI, August 1, 2012

SEE-Math: Strings & Probability

Philip B. Yasskin and David Manuel

Texas A&M University

We present the students with the following problem:
Imagine holding six strings in your fist with one end of each string sticking out the top and the other end sticking out the bottom. However, you do not know which top end connects to which bottom end. You tie off two top ends, another two top ends and the last two top ends. Then you tie off two bottom ends, another two bottom ends and the last two bottom ends. When you open your fist, you will find the strings tied in one big loop, or two loops or three loops. What is the probability that the strings are in one loop?
The students first guess an answer. Then they do the experiment by working in pairs with real strings and collect the data on the blackboard. Finally, they compute the probability. By adding strings, the activity leads into induction and double factorials.

Spreadsheet for Data

Slideshow for 1 Loop       Slideshow for 3 Loops

© Philip B. Yasskin, 2012.
Last updated Aug 5, 2012