How to explain the Monty Hall problem to a disbeliever
michalpaszkiewicz.co.uk
How to explain the Monty Hall problem to a disbeliever
1–10 of 95 posts
Re: How to explain the Monty Hall problem to a disbeliever
#2The most intuitive and simple explanation that worked for me is:
* if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong
* if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one
therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it
Re: How to explain the Monty Hall problem to a disbeliever
#3The most intuitive and simple explanation that worked for me is: * if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong * if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it
Or to just imagine a 1000 boxes with the same problem formulation
Re: How to explain the Monty Hall problem to a disbeliever
#4The most intuitive and simple explanation that worked for me is: * if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong * if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it
Or to just imagine a 1000 boxes with the same problem formulation
And the key thing here is that all boxes except two gets removed, not only one.
Re: How to explain the Monty Hall problem to a disbeliever
#5The thing that is often de-emphasised in the presentation of the problem, in order to make it seem more mysteriously paradoxical, is that the presenter knows where the car is and this knowledge is always used perfectly. If the question always ended with "remember: Monty knows where the car is and will use this information", it would be more obvious.
Imagine a universe with many simultaneous Monty Hall clones playing at once in many studios, where Monty doesn't know and opens another door at random. If that door has the car behind it, Monty and contestant are both shot in the head and the studio burned down and erased from all records. This bloody culling of branches of the probabilities is the same as effected by giving Monty the knowledge and telling him to act on it.
Re: How to explain the Monty Hall problem to a disbeliever
#6The most intuitive and simple explanation that worked for me is: * if on the 1st try you choose the correct box (33% chance), then the one you can switch to will be wrong * if on the 1st try you choose the wrong box (66% chance), then the one you can switch to will be correct one therefore your goal is to pick the wrong box on the 1st try and then switch, and you have 66% chance to do it
Or to just imagine a 1000 boxes with the same problem formulation
That was a new spin to the explanation that I didn't think of before.
Re: How to explain the Monty Hall problem to a disbeliever
#7I love the Monty Hall problem because it's so unintuitive that even Paul Erdos struggled to believe it for a while.
> Vazsonyi ran the program 100,000 times. Erdos watched the results of the simulation. The simulation results indicated that by switching, the odds of winning are indeed two out of three. Finally, he was grudgingly convinced that switching was better. He did not like it but seeing was believing. He could not argue with the results.
Apparently he later called Ronald Graham and explained to him that he finally heard a proof of the problem that made perfect sense to him, which he explained to Graham. Graham said he didn't understand the proof at all, but was happy Erdos understood where he had been mistaken.
Re: How to explain the Monty Hall problem to a disbeliever
#81. Changing your mind gives you the opposite of your original choice. 2. Your original choice gives you a goat 2/3 of the time and a car 1/3 of the time.
3. So by switching you get a car 2/3 of the time and a goat 1/3 of the time.
Re: How to explain the Monty Hall problem to a disbeliever
#9For me the hangup was always the hidden rule: host won’t open a door with a car. That is unstated and remains unstated even in modern discussions of the problem (see Pinker’s “Rationality”). Once explicitly states the outcome becomes intuitive.
Re: How to explain the Monty Hall problem to a disbeliever
#10As a programmer, I wasn't convinced until I wrote a short program to simulate it. Then the penny finally dropped...