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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 ...
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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?
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 ...
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 ...
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 $\frac14$...
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 ...
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 ...
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. ...