The Prisoner Paradox: Examining the Relativity of Probability in Everyday Life

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Discussion Overview

The discussion revolves around the concept of probability, particularly in the context of survival rates and the implications of independent events. Participants explore the relativity of probability in various scenarios, including hypothetical situations involving daily survival probabilities and comparisons to coin flips and radioactive decay.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that if they have a 50% probability of dying each day, they can calculate the cumulative probability of death over multiple days, leading to a total probability approaching 1.
  • Another participant counters that each day's survival is independent, similar to flipping a coin, where the probability remains 50% regardless of previous outcomes.
  • A participant introduces the Unexpected Hanging Paradox as a related example, questioning the assumptions involved in predicting outcomes based on prior events.
  • Some participants argue that the probabilities can change based on new information or events, while others maintain that the initial probability remains constant until an event occurs.
  • There is a discussion about the implications of survival probabilities in real-world scenarios, such as actuary tables, which change as individuals age.
  • One participant presents a thought experiment involving an atom with a decay probability, questioning whether the probability remains constant despite the time elapsed since its creation.
  • Several participants engage in a meta-discussion about the nature of assumptions and self-reference in logical reasoning, comparing it to mathematical proofs and circular reasoning.

Areas of Agreement / Disagreement

Participants express differing views on whether probabilities can change based on prior events or remain constant. There is no consensus on the interpretation of probability in the scenarios discussed, and multiple competing views remain throughout the thread.

Contextual Notes

Some discussions involve assumptions that may not be explicitly stated, such as the independence of events and the implications of survival probabilities over time. The conversation also touches on the complexities of logical reasoning and self-reference, which may not be fully resolved.

Who May Find This Useful

This discussion may be of interest to those exploring concepts of probability, mathematical reasoning, and philosophical implications of decision-making under uncertainty.

  • #31
Update -- user @AplanisTophet has left us, so thread it reopened.
 
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  • #32
berkeman said:
Update -- user @AplanisTophet has left us, so thread it reopened.
I was thinking of starting a new thread as the original OP was not he half as interesting as fresh_42 's prisoner link and Peroks explanations.
 
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  • #33
pinball1970 said:
I was thinking of starting a new thread as the original OP was not he half as interesting as fresh_42 's prisoner link and Peroks explanations.
I'm on a train with no WiFi, but I can post my analysis tomorrow if you start a thread on the prisoner paradox.
 
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  • #34
PeroK said:
I'm on a train with no WiFi, but I can post my analysis tomorrow if you start a thread on the prisoner paradox.
Great will do.
 
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