Should I Switch My Choice in the Monty Hall Problem?

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Discussion Overview

The discussion revolves around the Monty Hall problem, specifically whether a contestant should switch their choice after one door is revealed to contain a goat. Participants explore the implications of probability before and after a door is opened, examining the reasoning behind the probabilities assigned to the remaining doors.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that after revealing a goat behind one door, the probabilities should be 50% for the remaining doors, questioning the logic of the Monty Hall problem.
  • Another participant counters that the initial choice retains a probability of 1/3, while the remaining door's probability increases to 2/3, maintaining that switching is the better strategy.
  • A third participant confirms the 2/3 probability but notes that this conclusion relies on knowing the host's behavior, implying that variations in the game could affect the outcome.
  • Another participant elaborates on the reasoning by presenting a hypothetical scenario with 1000 doors, arguing that switching remains advantageous even in a larger context.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of probabilities after a door is opened. While some support the 2/3 probability for the remaining door, others question this conclusion, leading to an unresolved debate.

Contextual Notes

Some assumptions regarding the host's behavior and the initial conditions of the game are not fully explored, which may influence the interpretations of the probabilities discussed.

chhitiz
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in 21, when kevin spacey plays 'the 3 doors' with the lead character in a classroom, the guy says something like:"before you opened the door, the probability of each door having a car was 33.33% but now since door 3 has a goat and i have door1, the probability of door 2 adds up to 66.66% so i will take door 2 now." shouldn't the probability have become 50% for both doors?
 
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No! When door 1 was chosen, it had a probability of 1/3. Opening door 3 doesn't change that. Therefore door 2 has a probability of 2/3.
 
It sounds like you're referring to the classic Monty Hall problem. The answer is indeed 2/3 but it assumes that you know the host's behavior exactly.
 
Actually, door (2 or 3) had 2/3 probability. Now that door 3 has 0 prob after openning, prob of door 2 becomes 2/3.
To remove your confusion, think of 1000 doors behind one which there is a prize. You select one door and then 998 of the remaining doors are openned which are empty. Should you not then switch your choice?
 

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