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Related: Culture Forums, Support ForumsSince we're doing Math Games tonight ... how about this ... The Lets Make A Deal quandary!
Last edited Thu Aug 8, 2019, 06:20 PM - Edit history (1)
NO CHEATING AND LOOKING IT UP ON GOOGLE!!!
And try not give too much away in the comments if you KNOW the answer ... just make it sound like a guess til some people have a shot at it
Here's the math problem:
You are a contestant, Dolores, on the old game show, Monty Hall's Let's Make a Deal.
You reach the finale, where 3 doors are presented, and Monty tells you that behind the 3 doors are: A NEW CAR, A Goat, and an IRS Audit.
You're instructed to pick one of the 3 doors, and you do so. Say, it's door #1.
At this point, Monty opens either Door #2, revealing the Goat.
At this point, he says "You know Dolores, I like you. I'm going to give you a chance to change your mind and choose Door #3 ... Would you like to do that?"
Now ... there are two assumptions you should make in solving this problem:
1) Monty KNOWS what's behind each door, and does not want you to win the car, for whatever reason, thus will never reveal immediately that you've already won after your first pick.
2) Monty does not have a choice but to play the game in this fashion, it's just 'how it's done' in the game (which it really wasn't in the actual show, but this is for fun).
Oh, and
3) Winning a car is preferable to an IRS audit
Answer in the poll ... do you change your pick from #1 to #3?
And in the comments, explain why (without too much detail until some people have a chance to play )?
2 votes, 0 passes | Time left: Unlimited | |
I switch my choice to the other door | |
2 (100%) |
|
I do NOT switch my choice to the other door | |
0 (0%) |
|
Doesn't Matter Whether I Change, Odds are the Same | |
0 (0%) |
|
0 DU members did not wish to select any of the options provided. | |
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Disclaimer: This is an Internet poll |
Shrike47
(6,913 posts)I followed the instructions on how to bet.
mr_lebowski
(33,643 posts)In the original form of the published problem from 15 years back or so, the first 2 assumptions I added were not part of the question ... they've since been accepted as 'crucial', that's why I added them.
It's perhaps surprisingly a LOT more vague without those assumptions
cemaphonic
(4,138 posts)It's already an interesting counter-intuitive puzzle, but tying it to an actual show and personality just muddles it, since the real Monty Hall had considerable latitude in his behavior.
The always switch answer only works if Monty is a robot that behaves as you stipulated.
lapfog_1
(29,189 posts)by Marilyn vos Savant (Ask Marilyn) about this very question.
I say lucky because I was in an interview and the person asked me to solve the problem and I explained it just the way she explained it... and then told the interviewer that I had read the column so I already knew the correct answer.
I got the job offer.
mr_lebowski
(33,643 posts)The ensuing discussions over the years hence led me to add the assumptions in my version, as these were not part of her initial 'problem' ... and they should've been.
Still don't want anyone to cheat
cos dem
(902 posts)He has prior knowledge of the system. The fact that he will never open the door with the car behind it when it's his move is key.
Response to cos dem (Reply #5)
mr_lebowski This message was self-deleted by its author.
comradebillyboy
(10,128 posts)other door on the second guess. She wrote an article about this situation ten or twenty years ago. She was a major league bullshit artist but in this case her reasoning seemed sound.
mr_lebowski
(33,643 posts)this probability problem, and is the source of my bringing it up here.
And the public response to her original article is why I brought up the 'assumptions' to be made in figuring the solution.
TreasonousBastard
(43,049 posts)since this is a trick question the obvious answer is, of course, the wrong one.
Then I notice that two people who have seen this before say "switch". So why switch?
Again, and immediate assumption is that Monty would not give you the option to switch unless your first guess was the right one, now reducing your chances from 100% to 0%. Then I realized that everyone gets that choice.
So, digging round in ancient memories of useless knowledge, I found myself looking up things like Markov chains which reinforces my memories of there being no such thing as "random" that we can initiate, but only pseudo-random. Even a dice roll is influenced by outside forces and not simply probability, as is the roulette ball. Even in an honest game, a slight spin or slip can affect the odds.
Oh, and vos Savant never, ever writes a column mentioning things like Bayesian networks that will put her readers off. She specializes in relatively easy problems that make her readers feel smart once they get the trick.
So, I end up thinking that something in Monty's tone is giving you a huge hint what to do. He is trying to lead you astray and your real job is to figure out just what his "tell" is.
Then I cheat, and realize that increasing your odds from 50% to 66%, even if true, isn't worth worrying about.
BTW, I did lousy in college statistics. Considered changing my major from economics to something about sex. Maybe psychology.
mr_lebowski
(33,643 posts)Kick for the AM crowd...
KY_EnviroGuy
(14,488 posts)two errors in the description.
KY.........
mr_lebowski
(33,643 posts)KY_EnviroGuy
(14,488 posts)no mention of "goat" when you first listed the items behind the doors:
----
At this point, Monty opens either Door #2 or Door #3, revealing the Goat.
This may not be an error, but when you said Monty opened either door 2 or three, you didn't say which one (although that could be surmised later):
At this point, he says "You know Dolores, I like you. I'm going to give you a chance to change your mind and choose Door #3
We would therefore surmise that he actually opened Door #2 because he then gave you the choice of opening #3 (and suggesting a bias against opening #1 where the car would then most likely be found).
I am extremely tired so maybe too dense today.........
mr_lebowski
(33,643 posts)But the fact that he opened door #2 in this case revealing the donkey/goat should've been assumable when I said you're given a choice of door #3 ... but i'll fix that too
The assumptions to the problem are: he's biased against you winning (won't reveal you got it right the first time) and that he always conducts the game in this manner (i.e. he must reveal one crap prize, and he doesn't get to choose whether or not to allow you to switch, he always does that).
KY_EnviroGuy
(14,488 posts)............