Solving the 3Blue1Brown String Probability Problem (Without AI)

A probability puzzle from 3Blue1Brown asks for the expected number of loops created by randomly tying string ends from a box. The problem is approached with three different solutions to practice data science thinking. A brute-force probability tree is presented as a clunky method, followed by a more elegant mathematical solution that derives a formula by summing the probabilities of forming a loop in each independent round. Finally, a Monte Carlo simulation is demonstrated using Python code to approximate the answer, highlighting its utility for more complex problems without a clear closed-form solution.