Inside a square of side 2 units, five points are marked at random. What is the probability that there are at least two points such that the distance between them is at most sqrt{2} units?

Marcus Bass

Marcus Bass

Answered question

2022-09-26

Geometric probability
Inside a square of side 2 units , five points are marked at random. What is the probability that there are at least two points such that the distance between them is at most 2 units?

Answer & Explanation

Matthias Calhoun

Matthias Calhoun

Beginner2022-09-27Added 11 answers

Step 1
p = 0 because the furthest separation between 5 points in a square is with one at each corner and one in the middle, but by Pythagoras theorem the distance between the corner and the middle is 2 .
Step 2
Not a formal proof I grant you but the logic is infallible.
Kelton Molina

Kelton Molina

Beginner2022-09-28Added 1 answers

Step 1
Divide the square into 4 squares of side length 1.In at least one square there are two or more points.
Step 2
All points in the same square have distance less than 2 0.5 . So the answer is 1

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