Buffon's needle problem

Buffon's needle is a probabilistic problem that involves dropping a needle of a certain length onto a plane with parallel lines drawn at regular intervals. The problem was first posed by the French mathematician Georges-Louis Leclerc, Comte de Buffon, in the 18th century. Here's the set-up of the problem: 1. **Needle and Lines**: Imagine a plane with equally spaced parallel lines that are a distance \( d \) apart.