Grades 11-12 Video Solutions 2021-video 2021 11-12/18

Video Transcription

Video Summary

The problem involves determining the probability of a string, partially covered by three coins and capable of two overhead crossing manners at each coin, forming a knot when its ends are pulled. Each crossing has two options (over or under), leading to 2³ or eight possible crossing combinations. Only two combinations result in a valid overhand knot, specifically the left-handed and right-handed variants. Consequently, the probability of the string forming a knot is 2 out of 8, simplifying to 1 in 4, or 25%. Thus, the probability is one in four, corresponding to option B.

Keywords

probability

string knot

overhand knot

crossing combinations

coin crossings