# 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

123

## Answer

**Answers can only be viewed under the following conditions:**

- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.

Daniel90

436

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.

- answered
- 156 views
- $80.00

### Related Questions

- Calculating Dependant Probability of Multiple Events
- Combinatorical Drawing
- Convergence in Lp
- Probability question
- How do we define this choice function using mathematical notation?
- How to adjust for an additional variable.
- Goalscorer Probability question
- Probability maximum value of samples from different distributions