Non-countable uniform spaces probability

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Discussion Overview

The discussion revolves around the probability of randomly selecting a point within a circle such that the point is closer to the center than to the circumference. The context includes considerations from non-countable uniform spaces.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants question the method of selecting the point, suggesting that the choice of distribution affects the probability calculation.
  • Others emphasize the necessity of knowing a probability distribution to determine the probability of a randomly chosen point.
  • One participant clarifies the distinction between the center of the circle as a point and the radius as a numerical value without a specific location.
  • There is a request for clarification on whether a diagram is provided that designates a specific line segment as the radius.

Areas of Agreement / Disagreement

Participants express differing views on the implications of point selection and the definitions involved in the problem, indicating that multiple competing perspectives remain without a consensus.

Contextual Notes

There are unresolved assumptions regarding the method of point selection and the definitions of terms such as "radius" and "center," which may affect the interpretation of the problem.

Simonel
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A point is chosen at random inside a circle.Find the probability 'p' that the point chosen is closer to the center of the circle than to its radius.
This comes from the noncountable uniform spaces sections.
 
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Simonel said:
A point is chosen at random inside a circle.Find the probability 'p' that the point chosen is closer to the center of the circle than to its radius.
This comes from the noncountable uniform spaces sections.

It depends on how you choose the point, surely?

PS: I guess you mean closer to the centre than the circumference.
 
In or der to get the probability of a point chosen at random, requires knowing a probability distribution. This may sound a bit circular, but that's the way it is.
 
mathman said:
In or der to get the probability of a point chosen at random, requires knowing a probability distribution. This may sound a bit circular, but that's the way it is.
This is the way the problem is given and also the answer. :/
 
Simonel said:
This is the way the problem is given and also the answer. :/

The "center" of the circle is a point which has a location in 2D. The "radius" of a circle is a number, which has no particular location in 2D. A "radius" is not a particular line segment. Does the problem have a diagram where a particular line segment is designated as the radius?
 

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