The Monty Hall paradox/conundrum

  • Context: High School 
  • Thread starter Thread starter cmb
  • Start date Start date
  • Tags Tags
    Monty hall
Click For Summary

Discussion Overview

The discussion centers around the Monty Hall problem, specifically the probabilities associated with the decision to swap doors after one has been revealed to contain a goat. Participants explore the implications of the problem, debating the intuitive 50:50 probability versus the mathematically derived 2/3 probability when employing a swap strategy.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant argues that the probability of winning becomes 50:50 after the host reveals a goat, claiming that the initial 1/3 probability changes due to new information, invoking Bayesian reasoning.
  • Another participant counters this by presenting a hypothetical scenario with 1,000,000 doors, suggesting that the odds of winning do not change simply because the host reveals other doors, implying that the original choice remains at 1/1,000,000.
  • A third participant asserts that not all situations with two options result in 50:50 probabilities, emphasizing that the two options in the Monty Hall problem are not equivalent.
  • Some participants discuss the implications of changing the contestant and how knowledge of the original choice affects the probability assessment, with one suggesting that the new contestant would not have the same information as the original player.
  • Another participant emphasizes that the host's action of revealing a goat does not provide new information about the original choice, arguing that it does not warrant a change in the probability from 1/3 to 1/2.

Areas of Agreement / Disagreement

Participants express disagreement regarding the interpretation of probabilities in the Monty Hall problem. Some support the 50:50 conclusion, while others uphold the 2/3 probability when swapping doors. The discussion remains unresolved with competing views presented.

Contextual Notes

Participants reference various scenarios and interpretations of the problem, highlighting the complexity of probability assessments based on the host's actions and the information available to the contestants. The discussion reflects differing understandings of Bayesian probability and its application to the Monty Hall scenario.

  • #211
WWGD said:
I agree. What I mean is in the more general sense, if you're not sure you picked the goat, there is a 2/3 probability you did.
Yes. So if I didn't initially pick the car, then switching wins the car.
 
Physics news on Phys.org
  • #212
sysprog said:
Yes. So if I didn't initially pick the car, then switching wins the car.
Yes, I think we're both saying the same in different ways.
 

Similar threads

High School Monty Hall Paradox: Why Does It Matter What Host Knows?
  • · Replies 12 ·
Replies
12
Views
3K
High School Should You Stick or Switch? A Modified Monty Hall Problem
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Does Monty Fall change the odds in the Monty Hall problem?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Variation of Monty Hall problem
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad A variant of the Monty Hall problem
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Please Explain (actually explain) The Monty Hall Problem
  • · Replies 53 ·
2
Replies
53
Views
4K
Graduate Monty Hall: How Can the Host's Intentions Affect the Outcome of the Game?
  • · Replies 21 ·
Replies
21
Views
16K
Undergrad Why doesn't the solution to the Monty Hall problem make sense?
  • · Replies 89 ·
3
Replies
89
Views
11K
Undergrad Monty Hall Problem -- Questions
  • · Replies 30 ·
2
Replies
30
Views
4K
Undergrad Why the Monty Hall puzzle is categorically 1/2 and not 2/3rds
  • · Replies 38 ·
2
Replies
38
Views
8K