Single event probability equivalent to that of its permutations?

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Discussion Overview

The discussion revolves around the relationship between the probability of a specific event and the total probability of its permutations within a defined set of events. Participants explore whether the probability of an individual event can be equated to the sum of probabilities of all permutations that include that event, particularly in the context of a 2 x 2 square numbered 1 to 4.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions if the probability of a specific event, p(1), is equal to the total probability of all permutations including that event, suggesting a formula involving p(1,2), p(1,3), etc.
  • Another participant argues against the initial premise, stating that the question does not make sense and highlights the irrelevance of permutations to probability in this context.
  • A different participant introduces the binomial theorem to suggest that the total number of permutations including a specific event is greater than those excluding it, implying a relationship between events and their permutations.
  • Further clarification is sought regarding the definition of permutations and their relevance to the probability discussion.
  • A later reply acknowledges a misunderstanding and refers to the initial inquiry as a redundancy, indicating a shift in perspective.

Areas of Agreement / Disagreement

Participants express disagreement on the validity of equating event probabilities with permutations, with no consensus reached on the initial question or its implications.

Contextual Notes

There are unresolved assumptions regarding the definitions of probability and permutations, as well as the context in which they are applied. The discussion reflects varying interpretations of the relationship between events and their permutations.

Loren Booda
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Is the probability for a particular event, out of a set of events, equal to the total [normalized?] probability for all permutations of events from the set, including the particular event?

Say you have a 2 x 2 square with cells numbered 1 to 4. I am asking if the probability for square 1, p(1) is equal to the total probability for its permutations, p(1,2)+p(1,3)+p(1,4)+p(1,2,3)+p(1,2,4)+p(1,3,4)+p(1,2,3,4). Or should I divide this by the number of permutations?
 
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Loren Booda said:
Is the probability for a particular event, out of a set of events, equal to the total [normalized?] probability for all permutations of events from the set, including the particular event?

The answer is almost surely no, whatever question you meant to ask. Just suppose that something has zero probability.

Say you have a 2 x 2 square with cells numbered 1 to 4. I am asking if the probability for square 1,

This doesn't make sense. I have a square with 4 numbers. This is nothing to do with probabilities.

p(1) is equal to the total probability for its permutations, p(1,2)+p(1,3)+p(1,4)+p(1,2,3)+p(1,2,4)+p(1,3,4)+p(1,2,3,4). Or should I divide this by the number of permutations?


How is P(1,2) a permution of P(1)?
 
Consider this, demonstrable no doubt by the binomial theorem:

Given a set of events occurring with equal probability, the total number of permutations including a given event is one more than the total number of permutations without that event.
 
I'll say it again: the total number of permutations of what?

There are 6 permutations of the numbers 1,2,3 and 4 permutations of 1,2. You know, n!, right? And again, probability has nothing to do with this fact.
 
matt,

It turns out, upon further inspection, that what I was trying to describe is a redundancy. Sorry for the wild goose chase.
 

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