Q.6.3 - A First Course in Probability

Question

Suggest a procedure for using Buffon’s needle problem to estimate π. Surprisingly enough, this was once a common method of evaluating π. 

Step-by-Step Solution

Answer

Knowing L and D we can calculate $\mathrm{\pi }$.

Step 1: Content Introduction

Given a floor with evenly spaced parallel lines a distance d apart, Buffon's needle problem asks for the probability that a needle of length l would land on a line.

Step 2: Content Explanation

According to Buffon's needle problem

$P \{X<\frac{L}{2}\cos \left(\theta \right)\}=\frac{2L}{\mathrm{\pi D}}$

take a needle of length "L". draw a line equidistant at distance "D" on the table. Throw the needle on the table sufficiently large number of times. Calculate the probability by dividing the numbers of times needles cuts alone by the total number of times needle was thrown.

The probability is $\frac{2L}{\mathrm{\pi D}}$