# Probability of any random n points on a line being within a given distance

Given a virtual line segment in cm and n random points on it, what is the probability that the distance between any consecutive points on the line is less than a given minimum distance?

For Example:

n = 10 points

lineSegment = 1000 cm

minimumDistance = 2 cm

Running a Montecarlo simulation I took the following steps:

- generate n random points
- sort the points by order of smaller first
- calculate the distances between consecutive points
- count how many distances are smaller or equal to the minimumDistance.

Link to Python Montecarlo simulation on replit:

https://replit.com/@NissimCohen/MonteCarlo1#main.py

Is there an analytical solution to deal with any n number of points?

If yes, then I need:

1. Mathematical proof/explanation

2. algorithm/formula

Poincare

133

## Answer

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Daniel90

443

The answer is accepted.

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