The Monty Hall Problem only works this way if the host ALWAYS reveals a goat. That wasn't an established condition in either of their examples. If which door the game show host reveals is random (and could be a car) then the chance you're going to win whether you switch or not is 1/3 (as 1/3 the time the host will reveal the car and otherwise it's 50-50)
Technically you should still switch, but the probabilities are only right as a coincidence.
@Gastrophetes Actually according to the problem, the host knows whats behind the doors and will only reveal the goat. However, yes it is not explained in these scenarios
@Gastrophetes I was watching Sam Harris"Moral Landscape" and he posed this same question (goats, and all. Just like they did on 'Numb3rs".)My fiance walked in, paused it, and said "switch, what do YOU think?". I said what "average" people did... But my reasoning was that, even though the probability is greater, it's not guaranteed. By revealing the goat, that only suggests that the player chose the wrong 'door'. Am I wrong for thinking there's still a (small) chance "I" chose the right door?
And no you're not wrong for thinking there's still a chance you chose right initially (the chance is of course one third because there are 3 doors). If it helps consider each possibilities (there are only four).
If you switch: Given you chose car he shows goat you switch to goat and lose (1/3)
If you chose goat he shows goat and you switch to car and win (2/3)
If you don't: Given you chose car, you don't switch and win (1/3)
If you choose goat, you don't switch and lose (2/3)
@Gastrophetes THANK YOU!!!! TYTYTYTYTYTY! Since you illustrated the problem so beautifully, and efficiently, I'm DEFINITELY going to show your response/comment(s) to my fiance. I'm such a 'visual' person (artist/musician since childhood, but I was a die design engineer and auto-body stylist until the market went to crap... Go figure? LOL ;) Anyway, I can picture my thoughts in my noodle, but writing them out on paper, as you did, is more of a challenge. Ugh. Thanks, again. And again and again :D
@Gastrophetes What I also meant to say was that only one variable was removed by revealing the "goat"... Am I wrong, again? I like cold, hard facts. Probability doesn't strike my fancy, LOL. If I'm going to lose my money, say, I'd rather it be by spending it on something I know I'm going to get/keep, rather than 'probability". :/ Maybe I'm just an "average" person ;) So sue me!
It's not guaranteed either way. Monty Hall always opened the door with the goat. The idea here is that at the start you either choose a door with a goat (2/3 of the time) or a car (1/3 of the time). If he always shows a goat and never the car then if you chose a goat he will show the other goat leaving only the car to switch to (2/3 of the time). There are no guarantees, but you're twice as likely to win by switching because you're twice as likely to have originally chosen wrong.
The point is to double your chances of winning the prize, and yes it's not 100%, but 66.6% is better than 33.3% chance of winning the car.
Personally, I'd stay with my original choice if I were in a game show b/c it'd be a one-time thing and losing w/ my 1st choice is better (for me) than to lose w/ 2nd guessing.
But if I could do it in say 10 trials, then yes it'll switch 10 out of 10 times.
the teacher is wrong in the first example: the girl asks why and he says that you are most likely to have chosen the goat (he points to the 2nd card) and less likely to chosen the goat (he points to the 1st card). how did he came up with that conclusion? at the beginning you DONT know whats there, so ANY card is more likely for it being a goat, not just card 2, EVEN card 1, so the teacher is wrong here, but this whole problem is wrong anyway...
@ImageGround Since there are only 2 choices it the end comes down to two scenarios. Either you chose correctly initially and therefore shouldn't switch or you chose wrong initally and you should. Think about it, if you chose wrong initally and then a goat is revealed then you should switch (that's always going to be the case). Of course you'll never know for sure, but you know that your inital guess is probably wrong therefore it is probably in your interest to switch.
Huh... they both explained this incorrectly.
The Monty Hall Problem only works this way if the host ALWAYS reveals a goat. That wasn't an established condition in either of their examples. If which door the game show host reveals is random (and could be a car) then the chance you're going to win whether you switch or not is 1/3 (as 1/3 the time the host will reveal the car and otherwise it's 50-50)
Technically you should still switch, but the probabilities are only right as a coincidence.
Gastrophetes 3 months ago
@Gastrophetes Actually according to the problem, the host knows whats behind the doors and will only reveal the goat. However, yes it is not explained in these scenarios
Kevwho123 3 months ago
@Gastrophetes I was watching Sam Harris"Moral Landscape" and he posed this same question (goats, and all. Just like they did on 'Numb3rs".)My fiance walked in, paused it, and said "switch, what do YOU think?". I said what "average" people did... But my reasoning was that, even though the probability is greater, it's not guaranteed. By revealing the goat, that only suggests that the player chose the wrong 'door'. Am I wrong for thinking there's still a (small) chance "I" chose the right door?
eajoseph217 3 months ago
@eajoseph217
And no you're not wrong for thinking there's still a chance you chose right initially (the chance is of course one third because there are 3 doors). If it helps consider each possibilities (there are only four).
If you switch: Given you chose car he shows goat you switch to goat and lose (1/3)
If you chose goat he shows goat and you switch to car and win (2/3)
If you don't: Given you chose car, you don't switch and win (1/3)
If you choose goat, you don't switch and lose (2/3)
Gastrophetes 3 months ago
@Gastrophetes THANK YOU!!!! TYTYTYTYTYTY! Since you illustrated the problem so beautifully, and efficiently, I'm DEFINITELY going to show your response/comment(s) to my fiance. I'm such a 'visual' person (artist/musician since childhood, but I was a die design engineer and auto-body stylist until the market went to crap... Go figure? LOL ;) Anyway, I can picture my thoughts in my noodle, but writing them out on paper, as you did, is more of a challenge. Ugh. Thanks, again. And again and again :D
eajoseph217 3 months ago
@Gastrophetes What I also meant to say was that only one variable was removed by revealing the "goat"... Am I wrong, again? I like cold, hard facts. Probability doesn't strike my fancy, LOL. If I'm going to lose my money, say, I'd rather it be by spending it on something I know I'm going to get/keep, rather than 'probability". :/ Maybe I'm just an "average" person ;) So sue me!
eajoseph217 3 months ago
@eajoseph217
It's not guaranteed either way. Monty Hall always opened the door with the goat. The idea here is that at the start you either choose a door with a goat (2/3 of the time) or a car (1/3 of the time). If he always shows a goat and never the car then if you chose a goat he will show the other goat leaving only the car to switch to (2/3 of the time). There are no guarantees, but you're twice as likely to win by switching because you're twice as likely to have originally chosen wrong.
Gastrophetes 3 months ago
@eajoseph217
(you're too young to use that phrase).
Back on topic:
The point is to double your chances of winning the prize, and yes it's not 100%, but 66.6% is better than 33.3% chance of winning the car.
Personally, I'd stay with my original choice if I were in a game show b/c it'd be a one-time thing and losing w/ my 1st choice is better (for me) than to lose w/ 2nd guessing.
But if I could do it in say 10 trials, then yes it'll switch 10 out of 10 times.
R2Mintus 3 months ago
the teacher is wrong in the first example: the girl asks why and he says that you are most likely to have chosen the goat (he points to the 2nd card) and less likely to chosen the goat (he points to the 1st card). how did he came up with that conclusion? at the beginning you DONT know whats there, so ANY card is more likely for it being a goat, not just card 2, EVEN card 1, so the teacher is wrong here, but this whole problem is wrong anyway...
ImageGround 4 months ago
@ImageGround Since there are only 2 choices it the end comes down to two scenarios. Either you chose correctly initially and therefore shouldn't switch or you chose wrong initally and you should. Think about it, if you chose wrong initally and then a goat is revealed then you should switch (that's always going to be the case). Of course you'll never know for sure, but you know that your inital guess is probably wrong therefore it is probably in your interest to switch.
Limelightification 4 months ago
@ImageGround
Watch - hear the video more carefully and you'll understand... he dosn't say "less likely to chosen the goat (he points to the 1st card)"
GrigGrav 3 months ago
What season/episode is that ???
zardo4michael 6 months ago
much better the first explanation
PabloMaffioli 7 months ago