Probability of a needle of length L falling on a grid of parallel lines distance L apart crossing a line?

Probability of a needle of length L falling on a grid of parallel lines distance L apart crossing a line?

Approach: Integrate the angle and position of the needle.

2/π. This is Buffon's Needle problem.

Follow-up: How does the probability change if the needle length is L/2?

Key concepts: geometric probability, pi.