All Questions
Tagged with geometric-probability recreational-mathematics
10
questions
0
votes
1
answer
168
views
stick breaking, triangle and spacings
There is this famous problem:
Consider a stick of length 1. Pick two points uniformly at random on the stick, and break the stick at those points. What is the probability that the three segments ...
user617199
17
votes
3
answers
980
views
A random sphere containing the center of the unit cube
Inspired by a Putnam problem, I came up with the following question:
A point in randomly chosen in the unit cube, a sphere is then created using the random point as the center such that the sphere ...
- 645
0
votes
1
answer
65
views
Is sum of expected triangle areas equal to expected area of triangle sums?
Starting point
Given are 4 multinormal distributions $\mathcal{N}(\vec{\mu}_1,\Sigma), \mathcal{N}(\vec{\mu}_2,\Sigma),\mathcal{N}(\vec{\mu}_3,\Sigma),\mathcal{N}(\vec{\mu}_4,\Sigma)$ in $\mathbb{R^3}$...
- 523
2
votes
1
answer
76
views
Does expected triangle area change if a random point is added?
Starting point
Case I
There are 3 random points in a volume. Calculate the expected area of the triangle.
Case II
Calculate the expected area of any of the 4 triangles that are formed if a 4th random ...
- 523
5
votes
1
answer
100
views
Two points of a square $K$ determine a diagonal of another square that is contained in $K$
Let $K:=[0,1]^2$ be a square on $\mathbb{R}^{2}$. We select 2 random points $A$, $B$ $\in [0,1]^{2}$ in this square. What is the probability that the square whose diagonal is the line segment $AB$, is ...
- 139
15
votes
1
answer
607
views
How was "Number of ways of arranging n chords on a circle with k simple intersections" solved?
The problem whose solution is based on the solution to the problem in the title came up as I was trying to find a simpler variant of my needle problem.
I we were to uniformly, randomly and ...
- 12.5k
4
votes
0
answers
212
views
Randomly dropping needles in a circle?
If we were to randomly drop $n$ needles of random length in a circle,
what would be the odds of finding $k$ intersections? This can be asked
as:
Randomly place $n$ line segments in a circle. ...
- 12.5k
2
votes
0
answers
305
views
What is the average maximum value of a set of random numbers? [duplicate]
Let $a_1, a_2, a_3, \ldots, a_{10}$ be ten randomly chosen real numbers in the interval [0,1].
Let $m$ be the maximal value out of these 10 numbers.
What is the expected value of $m$?
(i.e. If i ...
- 1,261
50
votes
3
answers
2k
views
Expected number of people to not get shot?
Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle.
At midnight, each gangster shoots the person that is ...
- 1,261
4
votes
1
answer
451
views
Truchet tiles on a flattened cube
We have 2 Truchet tiles and a flattened cube as shown.
We randomly place copies of the tiles into faces of the flattened cube.
Find the probability that the circular arcs on the Truchet tiles will ...
- 41