Can you calculate probability with infinite sets?

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Discussion Overview

The discussion revolves around the calculation of probability within infinite sets, specifically examining the probability of selecting an odd number from a defined set of integers. The scope includes theoretical considerations of probability distributions and their applicability to infinite sets.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant proposes that the probability of choosing an odd number from a set defined by even integers and corresponding odd integers is 66%.
  • Another participant argues that calculating such a probability requires an appropriate probability distribution.
  • Several participants express confusion regarding the terminology and concepts related to probability distributions in the context of infinite sets.
  • It is suggested that there is no natural probabilistic method for selecting a member from a countably infinite set, and that uniform distribution is not applicable in this case.
  • A specific example is given where, if choosing uniformly from a finite subset, the probability of selecting an odd number approaches 2/3, but this does not extend to infinite sets.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the original claim regarding the probability of selecting an odd number, with multiple competing views on the necessity and nature of probability distributions for infinite sets.

Contextual Notes

Limitations include the lack of clarity on the definitions of probability distributions in infinite contexts and the unresolved nature of how to apply finite probability concepts to infinite sets.

gamow99
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Suppose set A is defined as the even integers and set B is defined as for every even integer there are two odd integers, like so: {2,3,3,4,5,5,6,7,7 ... }

Can you calculate that the probability of choosing an odd number is 66%?
 
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Not without an appropriate probability distribution.
 
Don't know what you mean.
 
In order to give a probability for something to happen you need to specify the probability distribution for the possible outcomes.
 
gamow99 said:
Don't know what you mean.
Then you should not have used the Intermediate classification for your thread. There is no natural probabilistic method for selecting a member from a countably infinite set.
If you choose uniformly from {2,3,3',4,5,5', ... 10^20) then the probability of selecting an odd is very close to 2/3. The uniform distribution is natural for a finite set, but there is no such for the infinite case.
 
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