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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?
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### 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 ...
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### 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 ...
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### 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. ...