I Monty Hall Problem -- Questions

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The Monty Hall problem illustrates that after an initial choice, switching doors increases the probability of winning the car from 1/3 to 2/3. This is based on the assumption that the placement of the car and goats is random, meaning the contestant's initial choice has a low likelihood of being correct. The discussion highlights confusion surrounding probability versus observed frequency, emphasizing that while randomness is a factor, the calculated probabilities remain consistent. Even if a contestant has biases in their choice, the underlying probabilities of the game are unaffected if the goats are placed randomly. Ultimately, the Monty Hall problem serves as a valuable example of probability theory, despite common misunderstandings.
  • #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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