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 2022-09-26 Answered
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?
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Answers (2)

Matthias Calhoun
Answered 2022-09-27 Author has 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.
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Kelton Molina
Answered 2022-09-28 Author has 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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