Monty Hall Problem -- Questions

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SUMMARY

The Monty Hall problem illustrates the counterintuitive nature of probability, specifically that switching doors after one is revealed increases the chance of winning from 1/3 to 2/3. Participants debated the implications of randomness in both the game and real-life scenarios, emphasizing that while the initial choice has a 1/3 chance of being correct, the act of revealing a goat alters the probabilities. The discussion highlighted the importance of understanding uniform randomness and how biases in choice do not affect the underlying probabilities of the game.

PREREQUISITES
  • Understanding of basic probability theory
  • Familiarity with the Monty Hall problem
  • Knowledge of uniform randomness in statistical analysis
  • Ability to differentiate between probability and observed frequency
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  • Study the mathematical foundations of the Monty Hall problem
  • Explore concepts of uniform vs. non-uniform randomness
  • Learn about Bayesian probability and its applications
  • Investigate real-world applications of probability theory in decision-making
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Mathematicians, statisticians, educators, and anyone interested in probability theory and its real-world implications will benefit from this discussion.

  • #31
WWGD said:
So you believe you can conceive every single possible correct solution?
No.

To defend that statement, which I thought I did pretty clearly, all I need to "conceive of" is one. By definition, to be "correct" another other solution must ultimately arrive at the same correct answer,1/(1+Q). If the contestant has no knowledge of where the car is, this is the most general, and correct, answer. Another solution can't both be correct, and get a different answer. (Note that 1/(1+Q) includes the less general, but correct, assumption that Q=1/2 so the probability is 2/3.)

Otherwise, we'd really have a paradox. So maybe you should go back to your imaginary world where mathematics doesn't have to be consistent.
 

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