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Questions tagged [geometric-probability]

Probabilities of random geometric objects having certain properties (enclosing the origin, having an acute angle,...); expected counts, areas, ... of random geometric objects. For questions about the geometric distribution, use (probability-distributions) instead.

Geometric probability is a tool to deal with the problem of infinite outcomes by measuring the number of outcomes geometrically, in terms of length, area, or volume. In basic probability, we usually encounter problems that are "discrete" (e.g. the outcome of a dice roll; see probability by outcomes for more). However, some of the most interesting problems involve "continuous" variables (e.g., the arrival time of your bus

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Pioneer probe´s distance to another star on its way out of the galaxy

I saw the question ”Finding the mean distance between n points evenly distributed in a disc of radius r” and I thought that some of the constants may be of use to my problem. My question is related to the pioneer 10 and 11 equipped with plaques…
Mikael Jensen
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Probability of center enclosed by polygon of random points

$N$ points chosen at random on the unit circle $x^2+y^2=1$. What is the probability that the center is enclosed by the convex polygon? Or rather the probability that the polygon formed by the $n$ points contains the origin? I of course tried the…
Randin
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Picking points inside a sphere

How to solve it? "Suppose that $N$ points are independently chosen at random inside a sphere of radius $R$. Find the probability of the distance between the center of the sphere and the closest point being greater than $r$, $r < R$, assuming the…
Gabriel Vivaldini
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geometric probability --- parallelograms

Inside a rhombus E with sides 10 unit and one interior angle less than 90 degree , there are 2 parallel ( with E ) parallelograms A and B , both can move freely and uniformly inside E but must keep parallel …
mrwong
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Ring thrown in space

A ring is thrown randomly in the space and let $A(t)$ be its position at moment $t$. Let us say that the moment $t_{0}$ is "twisted", if the ring $A(t_{0})$ is linked with the rings $A(t)$ for $t$ sufficiently close to $t_{0}$ $(t\neq t_{0})$.…
scholar
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Geometric Probability Problem, Random Numbers $0$-$1+$ Triangles.

Randy presses RANDOM on his calculator twice to obtain two random numbers between $0$ and $1$. Let $p$ be the probability that these two numbers and $1$ form the sides of an obtuse triangle. Find $p$. At first, I thought that the answer would be…
Hirnaeranin
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Probability of eventual success in independent trials (close form expression)

Consider a sequence of independent trials with success probability $p$. The formula for eventual success, i.e., there will be at least one success eventually, is $$ q = 1 - \prod_{n=1}^{\infty}{1-p(1-p)^{n-1}} $$ Is there a closed form expression…
Eracnet
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Three points on sides of equilateral triangle

Let's choose three points on the sides of an equilateral triangle(one point on each side) and construct a triangle with these three points. what is the probability that area of this triangle be at least one half of the area of equilateral triangle?
hossein Ghaffari
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Generate random numbers from appropriate distributions

Generate random numbers from appropriate distributions to find the area of the region enclosed by the curves y = sin (cos(x)), y = 0, x = pi/2 , and x = -pi/2 and report the area.
vishnu_18
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How is the Dehn invariant related to the mean width?

Reading Ravi Vakils Monthly article of february 2011 and watching the video; he mentions that the Dehn invariant is related to the linear invariant measure $\mu_1$ of geometric probability. The Klain Rota book discusses the Dehn invariant on pages…
Jan-Magnus Økland
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Probability density contour of bivariate normal distribution

I have a bivariate normal distribution and I want to determine the axes of the ellipse that will contain 60% probability. According to my textbok, It follows from the spectral decomposition of the covariance matrix (and the fact that the mahalanobis…
sid
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80% favors the building of a leisure center. Find the probability that the 7th Person is the 2nd person who is not in favor of the leisure centre.

For this question, I know I need to use Geometric Distribution. But I am lost because question asked for the 2nd person i.e 2nd occurrence instead of 1st occurrence. Appreciate anyone's help. Thanks!
mikhailcbh
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If two points are chosen at random on the circumference of the circle, find the probability that the selected points form the diameter of the circle.

Question: If two points are chosen at random on the circumference of the circle, find the probability that the selected points form the diameter of the circle. My thoughts: For the $2$ points to be the diameter of the circle, they must be…
user983440
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Geometric probability if the "good" area is an arc?

So I've been thinking about geometric probabilites and have a question that i don't know how to answer. So let's suppose we have $ABCD$ square with side lengths $1$. And we have a point $P$ inside the square. What is the probability that APB$\angle$…
math_inquiry
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Geometric Probability in Multiple Dimensions

I understand how Geometric Probability works in $1$, $2$, and $3$ dimensions, but is it possible to do these problems in, say, $5$ dimensions? For example, Five friends are to show up at a party from $1:00$ to $2:00$ and are to stay for $6$ minutes…
random guy 2000
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