The role of probability in solving the Monty Hall problem
March 8, 2016 at 7:38 pm
(This post was last modified: March 8, 2016 at 8:05 pm by Excited Penguin.)
I just read a post on WaitButWhy's blog and it's about a variation of the original Monty Hall problem that goes like this:
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Source - Monty Hall Problem
My contention is that you can only rely on probability in a controlled environment where you have knowledge of a certain definite pattern of choices that will always hold true(id est, e.g., you would have to know that out of 300 hundred such cases option one will be chosen one hundred times, option two one hundred times, and option three one hundred times as well and that this pattern would hold true no matter how many cases you would observe. . Then it would be logical to rely on probability, but otherwise, you have to keep in mind that for you the choice is totally random no matter what anyone does - unless someone actually tells you which one is the right one and you have 100% reason to trust them.
What would you think and can anyone convince me why it's still better to go with probability even if you don't have such(^^) knowledge?
For those who are interested in better understanding why one would think it's better to switch.
WaitButWhy: http://waitbutwhy.com/2016/03/the-jellyb...oblem.html
For anyone interested, here's the same argument I made on reddit about it, but talking about WBW's version of it:
https://www.reddit.com/r/WaitButWhy/comments/49es04/the_jelly_bean_problem/
----About the poll, some would argue that the I don't know option is just a variation of No when you get right down to it(at least in this particular case), but I put it in anyway for those of you that don't see it like that.
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
Source - Monty Hall Problem
My contention is that you can only rely on probability in a controlled environment where you have knowledge of a certain definite pattern of choices that will always hold true(id est, e.g., you would have to know that out of 300 hundred such cases option one will be chosen one hundred times, option two one hundred times, and option three one hundred times as well and that this pattern would hold true no matter how many cases you would observe. . Then it would be logical to rely on probability, but otherwise, you have to keep in mind that for you the choice is totally random no matter what anyone does - unless someone actually tells you which one is the right one and you have 100% reason to trust them.
What would you think and can anyone convince me why it's still better to go with probability even if you don't have such(^^) knowledge?
For those who are interested in better understanding why one would think it's better to switch.
WaitButWhy: http://waitbutwhy.com/2016/03/the-jellyb...oblem.html
For anyone interested, here's the same argument I made on reddit about it, but talking about WBW's version of it:
https://www.reddit.com/r/WaitButWhy/comments/49es04/the_jelly_bean_problem/
----About the poll, some would argue that the I don't know option is just a variation of No when you get right down to it(at least in this particular case), but I put it in anyway for those of you that don't see it like that.
