Linked Questions

1
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0answers
117 views

Probability of a triangle in a circle [duplicate]

I'm confused on my calculations on analytic geometry with probability. Things I learned on these were messed up since I was a newbie on these subjects. Here's my problem: Three points are chosen ...
18
votes
2answers
5k views

Probability that the convex hull of random points contains sphere's center

What is the probability that the convex hull of $n+2$ random points on $n$-dimensional sphere contains sphere's center?
4
votes
2answers
3k views

probabilty of random points on perimeter containing center

related question: probablity of random pick up three points inside a regular triangle which form a triangle and contain the center What is the probability that a (possibly degenerate) triangle made ...
4
votes
1answer
513 views

$n$ points are picked uniformly and independently on the unit circle. What is the probability the convex hull does not contain the origin? [duplicate]

We place $n$ points on the unit circle uniformly and independently . What is the probability that their convex hull does not contain the origin? I came up with this: I would greatly appreciate a ...
4
votes
1answer
370 views

Probability that a random triangle with vertices on a circle contains an arbitrary point inside said circle

What is the probability that a triangle with vertices uniformly randomly distributed on a circle contains the circle's centre? This is already done (similar to Putnam 1992 A6). The answer is $\frac14$...
5
votes
2answers
491 views

Writing a probability in terms of the edges of a simplex

I describe the problem dimension $2$, but it could be generalized to $n$ dimensions. So we have $X_{1}, X_{2}, X_{3}$ three $iid$ random variables of continuous law $F(x,y)$ on $\Bbb R^2$. Let's ...
1
vote
1answer
523 views

Geometric Probability- Circle and two points

A point $P$ is chosen $0.5$ units away from the centre of a circle of diameter $2$. Now two points are chosen randomly on the circumference of the circle. What is the probability that the triangle ...
0
votes
2answers
175 views

Probability that centre of circle is contained in triangle formed by three points on the circumference

I have been looking at this question. I thought I knew a solution, but it appears to be at odds with the answers there. Can anyone tell me what is wrong with my solution? My Attempted Solution. ...
0
votes
0answers
197 views

tetrahedrons, points, and spheres

this problem is a tricky one that i can't really sum up as a title, but this is the basic jist: a few days ago, my friend gave me this geometry problem: Given four random points on the surface of ...
0
votes
2answers
118 views

What's the probability that two randomly chosen points on a circle lie on the same diagonal?

At first, we pick a random point. Then there are infinite number of options for our next pick and only one point that is diagonally opposite to our first pick. Therefore, the probability is $\frac 1\...
0
votes
1answer
37 views

Probability that the center of a circle lies within three chosen points on a circle

The following question has been answered on MSE before and is indeed quite famous. I have one way of solving it and it seems quite wrong. Could anyone please help me correct it? Consider points $A$ ...