ISF Logo   IS Forum
Forum Index Register Members List Events Mark Forums Read Help

Go Back   International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology
 


Welcome to the International Skeptics Forum, where we discuss skepticism, critical thinking, the paranormal and science in a friendly but lively way. You are currently viewing the forum as a guest, which means you are missing out on discussing matters that are of interest to you. Please consider registering so you can gain full use of the forum features and interact with other Members. Registration is simple, fast and free! Click here to register today.
Tags math puzzles , probability , probability puzzles

Reply
Old 17th May 2019, 05:11 AM   #1
SumDooder
Student
 
Join Date: Jun 2018
Posts: 28
Probability Problem

So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.' He says 'each time there will be a 1 in 2 chance'. Which I kind of get, given there are two possible outcomes (sitting on my porch or not) to one event (him driving by my house). He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined. I assume there is some sort of fallacy involved saying out of two options they both have an equal chance of happening, but google is failing me. Does anyone have any good examples that demonstrate this fallacy?
SumDooder is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:23 AM   #2
The Great Zaganza
Maledictorian
 
The Great Zaganza's Avatar
 
Join Date: Aug 2016
Posts: 7,979
The easiest way to illustrate Monty Hall is to say there are a hundred doors, not three.
Monty opens all but two.
The chance has clearly switched from 1:100 to 1:2.
__________________
Opinion is divided on the subject. All the others say it is; I say it isn’t.
The Great Zaganza is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:25 AM   #3
lionking
In the Peanut Gallery
 
lionking's Avatar
 
Join Date: Jan 2007
Location: Melbourne
Posts: 43,541
There are several threads dedicated to this problem. I suggest searching them. Rehashing the same arguments can be tiresome.
__________________
A fanatic is one who can't change his mind and won't change the subject.

Sir Winston Churchill
lionking is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:25 AM   #4
GlennB
Loggerheaded, earth-vexing fustilarian
 
GlennB's Avatar
 
Join Date: Sep 2006
Location: Arcadia, Greece
Posts: 24,557
There being two possible outcomes doesn't necessarily mean those outcomes are equally probable. Roll two dice and you either will or will not roll 6-6. The chances of rolling 6-6 are 1 in 36.

If you, however, spend a random 50% of your time on the porch then he'd be right in calling the chances 1 in 2.
__________________
"Even a broken clock is right twice a day. 9/11 truth is a clock with no hands." - Beachnut
GlennB is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:27 AM   #5
GlennB
Loggerheaded, earth-vexing fustilarian
 
GlennB's Avatar
 
Join Date: Sep 2006
Location: Arcadia, Greece
Posts: 24,557
Originally Posted by lionking View Post
There are several threads dedicated to this problem. I suggest searching them. Rehashing the same arguments can be tiresome.
I don't think he's talking about Monty Hall specifically.
__________________
"Even a broken clock is right twice a day. 9/11 truth is a clock with no hands." - Beachnut
GlennB is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:48 AM   #6
SumDooder
Student
 
Join Date: Jun 2018
Posts: 28
Originally Posted by GlennB View Post
I don't think he's talking about Monty Hall specifically.
Yes, please. I only mention it in passing as where the conversation started.
SumDooder is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 05:59 AM   #7
MRC_Hans
Penultimate Amazing
 
MRC_Hans's Avatar
 
Join Date: Aug 2002
Posts: 21,997
Originally Posted by GlennB View Post
There being two possible outcomes doesn't necessarily mean those outcomes are equally probable. Roll two dice and you either will or will not roll 6-6. The chances of rolling 6-6 are 1 in 36.

If you, however, spend a random 50% of your time on the porch then he'd be right in calling the chances 1 in 2.
This.

Stating that there are two possibilities simply provide no useful information on the odds. There also is or is not an elephant in your front yard when he drives by.

Hans
__________________
Experience is an excellent teacher, but she sends large bills.
MRC_Hans is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:08 AM   #8
Myriad
Hyperthetical
 
Myriad's Avatar
 
Join Date: Nov 2006
Location: A pocket paradise between the sewage treatment plant and the railroad
Posts: 14,786
There is either a flying saucer crew from the Omicron Persei system doing an interplanetary survey in my back yard right now, or there isn't. I haven't checked.

Fifty-fifty?
__________________
A zømbie once bit my sister...
Myriad is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:24 AM   #9
Dave Rogers
Bandaged ice that stampedes inexpensively through a scribbled morning waving necessary ankles
 
Dave Rogers's Avatar
 
Join Date: Jan 2007
Location: Cair Paravel, according to XKCD
Posts: 28,960
Originally Posted by Myriad View Post
There is either a flying saucer crew from the Omicron Persei system doing an interplanetary survey in my back yard right now, or there isn't. I haven't checked.

Fifty-fifty?
Well, in fact, there's information there that can be used to form at least a vague estimate of the probabilities involved. Since none of us has ever seen a f.s.c.f.t.O.P.s, and history doesn't record one ever being seen, we would typically form an initial estimate that the odds were vanishingly small. On the other hand, since people are known to sit on porches, an initial estimate might be that the odds against are not too great - unless, of course, SumDooder's house doesn't actually have a porch, in which case we go back to vanishingly small. The point is that probability is about dealing with the level of uncertainty in the truth value of a statement, and it's very difficult to make a statement that conveys no information whatsoever as to its probability.

Dave
__________________
Me: So what you're saying is that, if the load carrying ability of the lower structure is reduced to the point where it can no longer support the load above it, it will collapse without a jolt, right?

Tony Szamboti: That is right
Dave Rogers is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:27 AM   #10
p0lka
Graduate Poster
 
Join Date: Sep 2012
Posts: 1,376
Originally Posted by The Great Zaganza View Post
The easiest way to illustrate Monty Hall is to say there are a hundred doors, not three.
Monty opens all but two.
The chance has clearly switched from 1:100 to 1:2.
The chance you are on the car is still 1/100, the chance the other door left is the car is 99/100, so you should swap. Where did the 1/2 come from?
p0lka is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:32 AM   #11
JoeMorgue
Self Employed
Remittance Man
 
JoeMorgue's Avatar
 
Join Date: Nov 2009
Location: Florida
Posts: 17,552
Again this is why I think the Three Prisoner Problem demonstrates it better then the Monty Hall Problem.

In the Monty Hall Problem people tend to get hung up on two factors; whether or not Monty is being honest and the fact that the individual can change their choice midway into the problem.

The Three Prisoner Problem removes those variables and still retains the same counter-intuitive nature.
__________________
- "Ernest Hemingway once wrote that the world is a fine place and worth fighting for. I agree with the second part." - Detective Sommerset
- "Stupidity does not cancel out stupidity to yield genius. It breeds like a bucket-full of coked out hamsters." - The Oatmeal
- "To the best of my knowledge the only thing philosophy has ever proven is that Descartes could think." - SMBC
JoeMorgue is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:50 AM   #12
theprestige
Penultimate Amazing
 
Join Date: Aug 2007
Posts: 34,099
It's just Bayes, isn't it?

You modify your estimate based on other assumptions and new information.

Either I'm a dog or I'm not. If you don't know a lot about dogs, you might provisionally put the probability of me being a dog much higher than someone who does know a lot about dogs.

And that's okay.
theprestige is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:54 AM   #13
The Great Zaganza
Maledictorian
 
The Great Zaganza's Avatar
 
Join Date: Aug 2016
Posts: 7,979
Originally Posted by p0lka View Post
The chance you are on the car is still 1/100, the chance the other door left is the car is 99/100, so you should swap. Where did the 1/2 come from?
you are right -
I stand corrected.
__________________
Opinion is divided on the subject. All the others say it is; I say it isn’t.
The Great Zaganza is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 06:58 AM   #14
Robin
Philosopher
 
Join Date: Apr 2004
Posts: 9,524
Originally Posted by SumDooder View Post
So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.' He says 'each time there will be a 1 in 2 chance'. Which I kind of get, given there are two possible outcomes (sitting on my porch or not) to one event (him driving by my house). He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined. I assume there is some sort of fallacy involved saying out of two options they both have an equal chance of happening, but google is failing me. Does anyone have any good examples that demonstrate this fallacy?
Tossing a bent coin. It will either land heads or tails, but the probability is not 0.5 heads and 0.5 tails.

In fact most texts will introduce coin examples with "assume a fair coin". My old uni statistics text calls statistics a "semi-empirical" branch of mathematics for this reason.
__________________
The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
Robin is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 07:04 AM   #15
Thermal
Philosopher
 
Thermal's Avatar
 
Join Date: Aug 2016
Location: NJ USA. We Don't Like You Either
Posts: 7,562
Originally Posted by p0lka View Post
The chance you are on the car is still 1/100, the chance the other door left is the car is 99/100, so you should swap. Where did the 1/2 come from?
It's a relativistic game. The odds are fiddy fiddy for any observer who did not know which door you picked, whether they were there at the beginning or walked in when there were only two left. But you have the additional information of the process of elimination which changes the odds from your perspective.
__________________
"Half of what he said meant something else, and the other half didn't mean anything at all" -Rosencrantz, on Hamlet
Thermal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 07:06 AM   #16
Robin
Philosopher
 
Join Date: Apr 2004
Posts: 9,524
Originally Posted by JoeMorgue View Post
Again this is why I think the Three Prisoner Problem demonstrates it better then the Monty Hall Problem.

In the Monty Hall Problem people tend to get hung up on two factors; whether or not Monty is being honest and the fact that the individual can change their choice midway into the problem.

The Three Prisoner Problem removes those variables and still retains the same counter-intuitive nature.
With the Monty Hall problem you can stipulate that the rules state that Monty has to offer the chance to change and this makes it irrelevant as to whether or not Monty is honest.
__________________
The non-theoretical character of metaphysics would not be in itself a defect; all arts have this non-theoretical character without thereby losing their high value for personal as well as for social life. The danger lies in the deceptive character of metaphysics; it gives the illusion of knowledge without actually giving any knowledge. This is the reason why we reject it. - Rudolf Carnap "Philosophy and Logical Syntax"
Robin is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 07:44 AM   #17
Thermal
Philosopher
 
Thermal's Avatar
 
Join Date: Aug 2016
Location: NJ USA. We Don't Like You Either
Posts: 7,562
Originally Posted by SumDooder View Post
So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.' He says 'each time there will be a 1 in 2 chance'. Which I kind of get, given there are two possible outcomes (sitting on my porch or not) to one event (him driving by my house). He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined. I assume there is some sort of fallacy involved saying out of two options they both have an equal chance of happening, but google is failing me. Does anyone have any good examples that demonstrate this fallacy?
If your house is underwater, I propose that the odds are slim you will be sitting on the porch.

If you mean your neighborhood is a dive, the odds are slim your buddy wants to go there anyway.

QED
__________________
"Half of what he said meant something else, and the other half didn't mean anything at all" -Rosencrantz, on Hamlet
Thermal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 08:23 AM   #18
Trebuchet
Penultimate Amazing
 
Trebuchet's Avatar
 
Join Date: Nov 2003
Location: The Great Northwet
Posts: 21,077
Here's a money-making opportunity: When you cut a deck of cards, the result will either be the six of spades or not. So, according to the friend, it's 50-50. See if you can get him to bet.
__________________
Cum catapultae proscribeantur tum soli proscripti catapultas habeant.
Trebuchet is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 08:27 AM   #19
JoeMorgue
Self Employed
Remittance Man
 
JoeMorgue's Avatar
 
Join Date: Nov 2009
Location: Florida
Posts: 17,552
Originally Posted by Trebuchet View Post
Here's a money-making opportunity: When you cut a deck of cards, the result will either be the six of spades or not. So, according to the friend, it's 50-50. See if you can get him to bet.
Pretty sure that you just proved immortality.
__________________
- "Ernest Hemingway once wrote that the world is a fine place and worth fighting for. I agree with the second part." - Detective Sommerset
- "Stupidity does not cancel out stupidity to yield genius. It breeds like a bucket-full of coked out hamsters." - The Oatmeal
- "To the best of my knowledge the only thing philosophy has ever proven is that Descartes could think." - SMBC
JoeMorgue is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 08:55 AM   #20
theprestige
Penultimate Amazing
 
Join Date: Aug 2007
Posts: 34,099
Originally Posted by Trebuchet View Post
Here's a money-making opportunity: When you cut a deck of cards, the result will either be the six of spades or not. So, according to the friend, it's 50-50. See if you can get him to bet.
His friend isn't stupid, so he probably won't agree to that bet. From the OP:
He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined.
The friend clearly understands the need to account for additional information when assessing probability. His argument is that when given an binary choice with no additional information, or with information that does not further clarify the probability, the starting estimate is going to be 50/50. Then that estimate will change as more information is added. This seems perfectly cromulent to me.

In reality, of course, more information is almost always present - or assumed to be present - at the start anyway.

I already know a lot about decks of cards, such as tarot cards, or the kind of playing cards that are customarily used for this kind of activity. So I would not take the bet. Not because the friend's reasoning is flawed, but because the friend's reasoning provides for adjusting the estimated probability based on additional information.

Trebuchet's money-making "opportunity" rests on taking only the first half of the friend's argument, and ignoring the second.

This isn't really a question about probability. It's a question of how we assign likelihood as a cognitive heuristic. What I want to know is, is it even possible to have a "raw" likelihood, without any modifying information? The friend's argument seems correct but largely academic. In the real world, phenomena carry too much baggage to admit a baggage-free starting probability.
theprestige is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 08:56 AM   #21
p0lka
Graduate Poster
 
Join Date: Sep 2012
Posts: 1,376
Originally Posted by Thermal View Post
It's a relativistic game. The odds are fiddy fiddy for any observer who did not know which door you picked, whether they were there at the beginning or walked in when there were only two left. But you have the additional information of the process of elimination which changes the odds from your perspective.
I'm not sure that is correct?
For instance, if you write down all the permutations for each door you start with, objectively in 99 of those permutations you end up on a goat and only in 1 permutation you are on a car, so swapping is objectively the correct thing to do.
Any observer who walks in at the end and just sees your door and one other, if they think it's 50/50 they're wrong, and it can be demonstrated they're wrong by again just writing down all the permutations, including the observer picking your door 50% of the time and picking the other door 50% of the time.

If their odds were indeed 50/50 then they would end on the car half the time, but they obviously won't for the same reason the player doesn't end on the car half the time, but on a goat 99 times out of the 100.

Last edited by p0lka; 17th May 2019 at 09:01 AM.
p0lka is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:17 AM   #22
Thermal
Philosopher
 
Thermal's Avatar
 
Join Date: Aug 2016
Location: NJ USA. We Don't Like You Either
Posts: 7,562
Originally Posted by p0lka View Post
I'm not sure that is correct?
For instance, if you write down all the permutations for each door you start with, objectively in 99 of those permutations you end up on a goat and only in 1 permutation you are on a car, so swapping is objectively the correct thing to do.
Any observer who walks in at the end and just sees your door and one other, if they think it's 50/50 they're wrong, and it can be demonstrated they're wrong by again just writing down all the permutations, including the observer picking your door 50% of the time and picking the other door 50% of the time.

If their odds were indeed 50/50 then they would end on the car half the time, but they obviously won't for the same reason the player doesn't end on the car half the time, but on a goat 99 times out of the 100.
The independent observer would choose the car half the time, assuming he knew nothing of the process of elimination. He has a one or the other choice, I'm pretty sure.
__________________
"Half of what he said meant something else, and the other half didn't mean anything at all" -Rosencrantz, on Hamlet
Thermal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:29 AM   #23
p0lka
Graduate Poster
 
Join Date: Sep 2012
Posts: 1,376
Originally Posted by Thermal View Post
The independent observer would choose the car half the time, assuming he knew nothing of the process of elimination. He has a one or the other choice, I'm pretty sure.
We already know that out of the 100 permutations, the player is on a goat 99 times and on the car 1 time.
The observer picks the players door in 50 of those permutations and the other door in the other 50 permutations, it's not possible for the observer to be on the car half the time, when we also know that the observer has picked the players door half the time.
p0lka is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:34 AM   #24
Hellbound
Merchant of Doom
 
Hellbound's Avatar
 
Join Date: Sep 2002
Location: Not in Hell, but I can see it from here on a clear day...
Posts: 13,427
Originally Posted by p0lka View Post
We already know that out of the 100 permutations, the player is on a goat 99 times and on the car 1 time.
The observer picks the players door in 50 of those permutations and the other door in the other 50 permutations, it's not possible for the observer to be on the car half the time, when we also know that the observer has picked the players door half the time.
I think you're missing that the newcomer does not know how the other 98 doors were opened. IOW, it could be that the player got 99 picks at doors, and the one he's on now is his last.

The odds only change if you have the knowledge of how the other doors were opened.

ETA: Or more accurately, the newcomer can only evaluate the odds on the basis of information he has; if he doesn;t know how the process worked that got them down to 2 doors, he can't evaluate the odds accurately.
__________________
Ideologies separate us. Dreams and anguish bring us together. - Eugene Ionesco

Last edited by Hellbound; 17th May 2019 at 09:35 AM.
Hellbound is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:35 AM   #25
psionl0
Skeptical about skeptics
 
psionl0's Avatar
 
Join Date: Sep 2010
Location: 31°57'S 115°57'E
Posts: 14,336
Originally Posted by SumDooder View Post
So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.' He says 'each time there will be a 1 in 2 chance'. Which I kind of get, given there are two possible outcomes (sitting on my porch or not) to one event (him driving by my house). He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined. I assume there is some sort of fallacy involved saying out of two options they both have an equal chance of happening, but google is failing me. Does anyone have any good examples that demonstrate this fallacy?
It is not a fallacy. If you have no information about the outcome of a trial whatsoever except that it may or may not happen then it is valid to assign a probability of 0.5 to that outcome.

The thing is that we actually have a lot of information about people sitting on porches and others have mentioned some of the factors that may influence the probability of seeing somebody sitting on a porch. We may not be able to give a reliable estimate of the probability but from what we can deduce, we can reliably say the the probability would be less than 0.5.

"Perceived" and "actual" odds is not a thing. What we have is "conditional" probability. That means the probability of an outcome depends (usually) on the conditions of the trial. In fact, there is no such thing as "unconditional" probability. A common condition is that there is a number of outcomes of equal probability and that the outcome is random. In a coin toss for example, we say that heads or tails is equally likely and don't consider things like the coin landing on its edge or snatched mid-air or being tossed by a cheat etc.
__________________
"The process by which banks create money is so simple that the mind is repelled. Where something so important is involved, a deeper mystery seems only decent." - Galbraith, 1975
psionl0 is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:52 AM   #26
p0lka
Graduate Poster
 
Join Date: Sep 2012
Posts: 1,376
Originally Posted by Thermal View Post
The independent observer would choose the car half the time, assuming he knew nothing of the process of elimination. He has a one or the other choice, I'm pretty sure.
Ah, I think you are correct, I just had another think about it, doh, sorry.





Originally Posted by Hellbound View Post
I think you're missing that the newcomer does not know how the other 98 doors were opened. IOW, it could be that the player got 99 picks at doors, and the one he's on now is his last.

The odds only change if you have the knowledge of how the other doors were opened.

ETA: Or more accurately, the newcomer can only evaluate the odds on the basis of information he has; if he doesn;t know how the process worked that got them down to 2 doors, he can't evaluate the odds accurately.
Yeah, I confused myself, sorry.
p0lka is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:55 AM   #27
Hellbound
Merchant of Doom
 
Hellbound's Avatar
 
Join Date: Sep 2002
Location: Not in Hell, but I can see it from here on a clear day...
Posts: 13,427
Originally Posted by p0lka View Post
Ah, I think you are correct, I just had another think about it, doh, sorry.







Yeah, I confused myself, sorry.
No worries. I do that all the time, especially on probability questions
__________________
Ideologies separate us. Dreams and anguish bring us together. - Eugene Ionesco
Hellbound is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 10:50 AM   #28
Brainster
Penultimate Amazing
 
Brainster's Avatar
 
Join Date: May 2006
Posts: 16,487
Originally Posted by SumDooder View Post
So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.'
There is no chance that you are sitting on your porch if you are driving by, because you are obviously in your car.

As for your problem with the Monte Hall puzzle, the simplest way to prove it's better to switch is to sit down with your friend and play it out a few times.
__________________
My new blog: Recent Reads.
1960s Comic Book Nostalgia
Visit the Screw Loose Change blog.

Last edited by Brainster; 17th May 2019 at 10:53 AM.
Brainster is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 11:59 AM   #29
Mike!
Official Ponylandistanian National Treasure. Respect it!
 
Mike!'s Avatar
 
Join Date: May 2010
Location: Ponylandistan! Where the bacon grows on trees! Can it get any better than that? I submit it can not!
Posts: 31,453
What about the box Carol Merrill just brought out?
__________________
"Never judge a man until you’ve walked a mile in his shoes...
Because then it won't really matter, you’ll be a mile away and have his shoes."
Mike! is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 12:09 PM   #30
theprestige
Penultimate Amazing
 
Join Date: Aug 2007
Posts: 34,099
Originally Posted by Mike! View Post
What about the box Carol Merrill just brought out?
Gwyneth Paltrow's head.
theprestige is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 01:49 PM   #31
GnaGnaMan
Graduate Poster
 
Join Date: Sep 2008
Posts: 1,572
Originally Posted by SumDooder View Post
So I've been going back and forth with a friend of a friend online regarding the Monte Hall Problem. It has devolved into disagreements about probabilities and I'm having a hard time. He has gone into 'actual' and 'perceived' odds. My latest example is 'When you dive by my house, I'm either sitting on the porch or I'm not. What is the probability I am sitting on my porch when I drive by.' He says 'each time there will be a 1 in 2 chance'. Which I kind of get, given there are two possible outcomes (sitting on my porch or not) to one event (him driving by my house). He calls those 'actual' odds while 'perceived' odds can't be calculated until my parch sitting habits are examined. I assume there is some sort of fallacy involved saying out of two options they both have an equal chance of happening, but google is failing me. Does anyone have any good examples that demonstrate this fallacy?
There are 2 ways of understanding probabilities: Frequentist and Bayesian.

The frequentist view is that a probability is information about how often something happens; or the frequency at which something happens. If you told a frequentist that you sit on the porch 1 hour each day, then he would say that the probability of finding you on the porch at any time during the day is 1/24.
Without any such information, the frequentist would deny that the question makes sense: You either sit on the porch or you don't. The probability is either 0 or 1 and we simply don't know either way.

The Bayesian view is more abstract. Probability is a statement about your knowledge or lack thereof.
Under this view you could just pull a number out of your ass. You could say: At this time of day, almost no one sits on the porch so the probability is 5%.
Or you could say:He knows I'm coming so he's probably waiting on the porch. The probability is 80%.
If you really don't know either way you might as well chose 50/50.
Neither number is right or wrong in any mathematical sense. Bayesian statistics provides mathematical methods to refine the initial guess (called prior probability) with empirical data. Every time you drive past the porch and see someone sitting there or not, your guess is nudged closer to the true value, regardless of how right or wrong your initial guess was.
How to best come up with a prior is subject to contentious debate. https://en.wikipedia.org/wiki/Prior_...rmative_priors
__________________
It makes no difference whatever whether they laugh at us or revile us, whether they represent us as clowns or criminals; the main thing is that they mention us, that they concern themselves with us again and again. -Hitler
GnaGnaMan is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 17th May 2019, 09:07 PM   #32
caveman1917
Philosopher
 
Join Date: Feb 2015
Posts: 6,103
Originally Posted by theprestige View Post
What I want to know is, is it even possible to have a "raw" likelihood, without any modifying information?
Just use the maximum entropy distribution where the given information is the empty set (ie "without any modifying information" to put it in your terms) - it works just as well when the information set is empty as when it isn't.
__________________
"Ideas are also weapons." - Subcomandante Marcos
"We must devastate the avenues where the wealthy live." - Lucy Parsons
"Let us therefore trust the eternal Spirit which destroys and annihilates only because it is the unfathomable and eternal source of all life. The passion for destruction is a creative passion, too!" - Mikhail Bakunin
caveman1917 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 09:20 AM   #33
bobdroege7
Master Poster
 
bobdroege7's Avatar
 
Join Date: May 2004
Posts: 2,650
So your friend is either on the porch or not, so it's 1 of 2.

So your friend is either on the porch, or on the sofa or on neither, so it's 1 of 3.

So your friend is either on the porch, or on the sofa or in the kitchen cooking dinner or none of those, so 1 in 4.
__________________
Un-american Jack-booted thug

Graduate of a liberal arts college!

Faster play faster faster play faster
bobdroege7 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 09:37 AM   #34
Thermal
Philosopher
 
Thermal's Avatar
 
Join Date: Aug 2016
Location: NJ USA. We Don't Like You Either
Posts: 7,562
I'm surprised no one has brought up the classic example:

When visiting Egypt, poster shemp is either dry-humping the Sphinx, or he is not. 50/50 odds?
__________________
"Half of what he said meant something else, and the other half didn't mean anything at all" -Rosencrantz, on Hamlet
Thermal is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 09:51 AM   #35
Jack by the hedge
Safely Ignored
 
Jack by the hedge's Avatar
 
Join Date: Oct 2009
Posts: 9,429
Originally Posted by Brainster View Post
There is no chance that you are sitting on your porch if you are driving by, because you are obviously in your car.
What are the chances he's sitting in his Porsche when he drives by?
Jack by the hedge is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 09:54 AM   #36
psionl0
Skeptical about skeptics
 
psionl0's Avatar
 
Join Date: Sep 2010
Location: 31°57'S 115°57'E
Posts: 14,336
Originally Posted by Thermal View Post
I'm surprised no one has brought up the classic example:

When visiting Egypt, poster shemp is either dry-humping the Sphinx, or he is not. 50/50 odds?
Well, we know a lot more about shemp than nothing so, not 50/50.
__________________
"The process by which banks create money is so simple that the mind is repelled. Where something so important is involved, a deeper mystery seems only decent." - Galbraith, 1975
psionl0 is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 10:04 AM   #37
Pope130
Master Poster
 
Pope130's Avatar
 
Join Date: Sep 2005
Location: Oregon
Posts: 2,953
Originally Posted by Jack by the hedge View Post
What are the chances he's sitting in his Porsche when he drives by?
What are the chances that a person who owns a Porsche is wasting his Sunday posting on the internet?
Pope130 is offline   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Old 19th May 2019, 10:05 AM   #38
psionl0
Skeptical about skeptics
 
psionl0's Avatar
 
Join Date: Sep 2010
Location: 31°57'S 115°57'E
Posts: 14,336
Originally Posted by bobdroege7 View Post
So your friend is either on the porch or not, so it's 1 of 2.

So your friend is either on the porch, or on the sofa or on neither, so it's 1 of 3.

So your friend is either on the porch, or on the sofa or in the kitchen cooking dinner or none of those, so 1 in 4.
That is similar to the fallacy used to prove that it is almost certain that there is life on planet X.

We have no knowledge of whether there are horses on planet X or not so the probability is 50%
We have no knowledge of whether there are cows on planet X or not so the probability is 50%
So the probability that there are neither horses nor cows on planet X is 50% x 50% = 25%.

Add all the other species of life on Earth in the mix and we can conclude that the probability that none of them exists on planet X -> 0% so it is almost certain that some form of life on planet X exists.

The flaw is that these are all conditional probabilities but we are not expressly told what conditions have been assumed.

The starting point is that the probability that life can be supported on planet X is 50%. The probability that life exists on planet X given that life can be supported on planet X is 50% etc etc.
__________________
"The process by which banks create money is so simple that the mind is repelled. Where something so important is involved, a deeper mystery seems only decent." - Galbraith, 1975

Last edited by psionl0; 19th May 2019 at 10:07 AM.
psionl0 is online now   Quote this post in a PM   Nominate this post for this month's language award Copy a direct link to this post Reply With Quote Back to Top
Reply

International Skeptics Forum » General Topics » Science, Mathematics, Medicine, and Technology

Bookmarks

Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Forum Jump


All times are GMT -7. The time now is 03:59 AM.
Powered by vBulletin. Copyright ©2000 - 2019, Jelsoft Enterprises Ltd.

This forum began as part of the James Randi Education Foundation (JREF). However, the forum now exists as
an independent entity with no affiliation with or endorsement by the JREF, including the section in reference to "JREF" topics.

Disclaimer: Messages posted in the Forum are solely the opinion of their authors.