Education In Thailand

[solo siam]

Its quite ironic that you sneer at the education of others when you're unaware that I've been describing a very famous mathematical problem known as "The Monty Hall Problem"

http://en.wikipedia.org/wiki/Monty_Hall_problem

That only works if the host knows whats behind ALL the doors and HAS to choose a door to reveal that doesn't contain the prize AND that the contestant knows he has to do that as part of the game, neither of which were pointed out in your initial post and are what underpins that entire 'mathematical problem'.

You are changing the probability because the host HAS to take away one of the losing doors.

[Khun Jean]

You can not compare a question about how many weeks in ten years with a question about probability.

The first needs only common knowledge and some basic calculations. The other needs a whole lot more than that.

But when you calculate the odds for a good answer actually the difficult one about the quiz master has 50% chance to be answered correctly.

The weeks in 10 years has a lot less probability if the common knowledge is lacking.

With the known 13 people (12 Thai and 1 foreigner (Sibeymay ) who have been asked this "weeks in ten year" question none of them had the right answer. If the difficult question was asked you probably would have 6-7 right answers.

Next time better ask a difficult question with only a yes/no as possible answers.

I asked a few more people this question and i counted another 8 wrong answers (all of them 480) and 1 almost good answer (520).

The persons where between 10 and 80 year olds. So it is save to say that common knowledge is there but the knowledge is wrong! I say that because the common knowledge is 4 weeks and 12 months. Not the 52 weeks in a year, that is mostly unknown. And there you have the real problem.

I think i stick with my decision to let my kids study in the western world!

[Theyreallrubbish]

Just asked a university educated Thai and got the exact same answer. 4*12*10= 480 weeks

Amazing

[elkangorito]

At my college, cheating is simply not tolerated.

How can you do it in the era of mobile devices?

Why is not the old scheme - the students get marks like 12th of 20 or whatever their ranking might be within their class?

That repels the cheating. Either everybody or nobody cheats.

At my college, cheating is simply not tolerated. This means that my college has not erradicated cheating. If someone is found to be cheating, they automatically fail.

Class ranking does not appear to exist in Thai government schools. Most classes have a large crossection of students, ranging from "hopeless" to "gifted". This makes for very frustrating teaching.

[dave111223]

Asked my wife the question, and she also answered 480 ("Because there are 4 weeks in a month").

We also have a Japanese friend staying and asked her the question and got 600 ("Because there are 5 weeks in a month").

[Stephen Cleary]

What is daftness?

Well, some Farangs are brought up to be decent with their statistical math while others are not.

As for Geography, a well publicized survey on this subject as re-published in the Bangkok Post recently found that 25% of Americans couldn't point out where the US where was on a world map.

As for the great Western Leaders, was it not George W Bush himself, who answered on that memorable radio interview when he was running for the Republican's replied to these two questions:

DJ: "Mr Senator-Elect, can you mention 5 capital cities in the world"

Bush: "Sure, i can. Washington, London, Paris, Berlin and mmmm..... Barcelona"

DJ: "Very interesting Sir that you mention Spain, have you enjoyed your visits there?"

Bush: "Actually, to tell you the truth, i've never been to South America"

Edited October 16, 2007 by Stephen Cleary

[Theyreallrubbish]

Its quite ironic that you sneer at the education of others when you're unaware that I've been describing a very famous mathematical problem known as "The Monty Hall Problem"

http://en.wikipedia.org/wiki/Monty_Hall_problem

That only works if the host knows whats behind ALL the doors and HAS to choose a door to reveal that doesn't contain the prize AND that the contestant knows he has to do that as part of the game, neither of which were pointed out in your initial post and are what underpins that entire 'mathematical problem'.

You are changing the probability because the host HAS to take away one of the losing doors.

Actually the hosts knowledge is not part of the actual problem. I said assuming its not the prize. If it is the prize you scrap the game and start again.

The host's knowledge is an entire different issue which is why the Monty Hall Problem is used as an illustration in gaming theory and taught as part of corporate strategy as an example of how to use assymetry of information to gain information.

But the mathematical problem as originally posed doesn't require host knowledge to still illustrate the mathematical principle, and your own replies illustrate very clearly what wikipedia describes as "a veridical paradox in the sense that the solution is counterintuitive."

I didn't know about veridical paradox so I've learned something new today as well

[sonnyJ]

Asked my wife the question, and she also answered 480 ("Because there are 4 weeks in a month").

We also have a Japanese friend staying and asked her the question and got 600 ("Because there are 5 weeks in a month").

Was that a humorous attempt?

[sonnyJ]

What is daftness?

Well, some Farangs are brought up to be decent with their statistical math while others are not.

As for Geography, a well publicized survey on this subject as re-published in the Bangkok Post recently found that 25% of Americans couldn't point out where the US where was on a world map.

As for the great Western Leaders, was it not George W Bush himself, who answered on that memorable radio interview when he was running for the Republican's replied to these two questions:

DJ: "Mr Senator-Elect, can you mention 5 capital cities in the world"

Bush: "Sure, i can. Washington, London, Paris, Berlin and mmmm..... Barcelona"

DJ: "Very interesting Sir that you mention Spain, have you enjoyed your visits there?"

Bush: "Actually, to tell you the truth, i've never been to South America"

Please reveal these "surveys". Origin of these statements, u surely must be a yank.

Soon surely 25% of these "americans" must be foreign, if not yet. So the QUESTION is what will you do about/for them in USA when they decide to reach for?

1. Be a President

2. Get genocided, sorry for spelling..

3. Just wanting to be legal aliens.

4. Or just suppressed the normal way.

So let's see.

SORRY OFF TOPIC

[llothar]

Besides how could it be 522? the most extra days from leap years would be 3, the answer can only be 521.

No the question does not contain the word "consecutive years" so 521 or 522 is correct

[dave111223]

Asked my wife the question, and she also answered 480 ("Because there are 4 weeks in a month").

We also have a Japanese friend staying and asked her the question and got 600 ("Because there are 5 weeks in a month").

Was that a humorous attempt?

No... why?

[TAWP]

Since it's 1/3 that you have picked the right door from the start, but 2/3 you have picked the wrong one...

Maths is obviously not the strong point of a lot of people here, by making another choice you have also only a 1/3 chance of picking the right one and 2/3 of picking the wrong one.

Any door has a 1/3 chance of being the 'correct door' at all times before any of the doors are opened, you are just swapping a 1/3 for a 1/3.

You should really not respond when you have no clue. It just makes you look silly.

Perhaps you missed the important aspect that after you picked the one door, one other (one that is wrong) is opened by the host. You now have 2 doors left. Do you keep your choice or switch?

People, this is basic high school math...

[solo siam]

Since it's 1/3 that you have picked the right door from the start, but 2/3 you have picked the wrong one...

Maths is obviously not the strong point of a lot of people here, by making another choice you have also only a 1/3 chance of picking the right one and 2/3 of picking the wrong one.

Any door has a 1/3 chance of being the 'correct door' at all times before any of the doors are opened, you are just swapping a 1/3 for a 1/3.

You should really not respond when you have no clue. It just makes you look silly.

Perhaps you missed the important aspect that after you picked the one door, one other (one that is wrong) is opened by the host. You now have 2 doors left. Do you keep your choice or switch?

People, this is basic high school math...

Actually if the host doesn't know what's behind all three doors, then the probability remains constant and its not worth switching. This problem only exists where the host knows whats behind ALL of the doors and HAS to pick a losing door to reveal and that the contestant knows this.

Mixing it up a bit. Two contestants choose a door, one after the other - the 2nd contestants door is opened first and is a loser, absolutely no reason at all for the first contestant to switch doors, identical probability (he now has a 1 in 2 chance of winning).

Edited October 17, 2007 by solo siam

[LinkPopularity]

If you saw Paris Hilton on TV in America would you assume that the whole school system is completly rubbish?

the American school system is rubbish !

[Mossfinn]

Education around the World is somewhat lacking...

Sign in an Pharmacy window in Oxford..

'We are going through a stage of refurbishment

Please bere bare with us'.

'nuff said

Moss

[TAWP]

Since it's 1/3 that you have picked the right door from the start, but 2/3 you have picked the wrong one...

Maths is obviously not the strong point of a lot of people here, by making another choice you have also only a 1/3 chance of picking the right one and 2/3 of picking the wrong one.

Any door has a 1/3 chance of being the 'correct door' at all times before any of the doors are opened, you are just swapping a 1/3 for a 1/3.

You should really not respond when you have no clue. It just makes you look silly.

Perhaps you missed the important aspect that after you picked the one door, one other (one that is wrong) is opened by the host. You now have 2 doors left. Do you keep your choice or switch?

People, this is basic high school math...

Actually if the host doesn't know what's behind all three doors, then the probability remains constant and its not worth switching. This problem only exists where the host knows whats behind ALL of the doors and HAS to pick a losing door to reveal and that the contestant knows this.

Mixing it up a bit. Two contestants choose a door, one after the other - the 2nd contestants door is opened first and is a loser, absolutely no reason at all for the first contestant to switch doors, identical probability (he now has a 1 in 2 chance of winning).

Cute dodge, but it doesn't change the fact that your lack of knowledge on the subject is what caused your first post.

(Btw, do tell how the host is supposed to open a door _not_ containing a car and show it to the contestant if he doesn't know which door the car actually hides behind...it would kinda ruin the gameshow if he picked the car-door. Which you would have known if you had known the classical question and/or the gameshow in question.)

[Payboy]

If you saw Paris Hilton on TV in America would you assume that the whole school system is completly rubbish?

no, but i would say my choice of the tv channel was completely rubbish

[Tony Clifton]

My wife answered 520.

[jstumbo]

Since it's 1/3 that you have picked the right door from the start, but 2/3 you have picked the wrong one...

Maths is obviously not the strong point of a lot of people here, by making another choice you have also only a 1/3 chance of picking the right one and 2/3 of picking the wrong one.

Any door has a 1/3 chance of being the 'correct door' at all times before any of the doors are opened, you are just swapping a 1/3 for a 1/3.

You should really not respond when you have no clue. It just makes you look silly.

Perhaps you missed the important aspect that after you picked the one door, one other (one that is wrong) is opened by the host. You now have 2 doors left. Do you keep your choice or switch?

People, this is basic high school math...

Actually if the host doesn't know what's behind all three doors, then the probability remains constant and its not worth switching. This problem only exists where the host knows whats behind ALL of the doors and HAS to pick a losing door to reveal and that the contestant knows this.

Mixing it up a bit. Two contestants choose a door, one after the other - the 2nd contestants door is opened first and is a loser, absolutely no reason at all for the first contestant to switch doors, identical probability (he now has a 1 in 2 chance of winning).

Cute dodge, but it doesn't change the fact that your lack of knowledge on the subject is what caused your first post.

(Btw, do tell how the host is supposed to open a door _not_ containing a car and show it to the contestant if he doesn't know which door the car actually hides behind...it would kinda ruin the gameshow if he picked the car-door. Which you would have known if you had known the classical question and/or the gameshow in question.)

Following the logic that your odds are better to change, then I guess this would work also?

If you pick #1, you have a 1/3 chance. They then open door #3 and it is the grand prize. So now I guess you still have a 1/3 chance that your door has the prize? Don't recalculate your odds given the new information about what was behind door #3, you don't do that if it is the booby prize. So even though you know that door #3 has the prize, you still have a 1/3 chance? And if you switch to door #2, you have a 2/3 chance? So the chances of the prize being in door #1 or door #2 is 3/3? Even though you have already opened up door # 3 and see the grand prize? So how can it be a 3/3 chance that it is in door #1 or #2, when you can look at the prize in door #3?

[jstumbo]

Here is a wheel that people use to explain the monty question. I have modified it because I feel that the original one is flawed.

The inner part is the door with the prize. The middle part is your choice, and the outside part is the door that monty opens. The red means that you should switch doors if you want to win and the blue means you should keep your door. The original of this wheel had two choices for each red section, both with the same door number. I felt like this part was flawed because why would monty have a choice of door #3 or door #3? He wouldnt, it would only be a choice of door #3.

So as an example, if the prize is behind door #1, then you pick door #1, monty can open either door #2 or door #3, and you should keep your choice to win. If however you pick door #2, monty can only open door #3 and if you do not change then you lose. If you pick door #3, then monty can only open door #2, and you would need to change to win. As you can see, there are 12 possibilities on where you could be sitting after monty opens a door. This assumes that he knows the door with the car and will not open it, so you get a chance to switch. 6 times you should stay with your door and 6 times you should change.

What if Monty did not know which door had the car and he could open the door with the car first? If he opened it first then you lose and are not given the chance to change. As you can see in the following wheel. The black would be where the door with the car was opened first. In this case game over. So 2/3 of the time, you would lose. But when given the chance to switch, you odds would be again 50:50.

[rychrde]

Perhaps I am misunderstanding this gameshow but why is it better to switch?

this is a very old problem and yet every generation still finds the result counter-intuitive.

http://www.gametheory.net/applets/probability.html

the above is a nice site with links to Monty Hall simulation and lots of other game theory stuff.

For the Monty Hall simulation, decide on one strategy and stick to it for maybe 20 goes, then switch strategy and compare the two results.

enjoy

rych

[madjbs]

I understand it if the game show host knows what door to pick. That information was lacking in the first post on the subject though.

[TAWP]

That would indicate that you didn't know about the game show and/or quiz from the start and would indicate a lack of basic wide education on your part.

(Have to state it since the thread attacks this quality in thais...)

[Theyreallrubbish]

That would indicate that you didn't know about the game show and/or quiz from the start and would indicate a lack of basic wide education on your part.

(Have to state it since the thread attacks this quality in thais...)

This was my reason for posting it in the first place. To show that what is considered common knowledge by some isn't by others and that people can make horrendous mistakes in mathematics by going by what feels likes the common sense answer to them. In the Thai's case that there are 4 weeks in a month, in our high and mighty fellow board posters, that every door always has a 1 in 3 chance.

[TAWP]

You have proven it well, and for that I salute you.

[madjbs]

I don’t know anything about this game show, so I could only go by what you said in your post (I assume its the same for the "high and mighty fellow board posters") So when people come to the wrong conclusion purely because they have been given incomplete information, why is it a horrendous mistake. It was in fact correct taking into account the information given.

And in the Thai game show case, I think it is more to do with the lack of intelligence of the contestants. I asked 7 people yesterday who attend a top university and they all got 520 except 1 person who said 720.

[A_Traveller]

As an aside this discussion has been going on for a long time, including comments for the eponymous Monty. By the by I recall this as the Three Prisoners Problem, not having ever seen the game show, which was posited in the late fifties/early sixties.

Regards

Excerpted from The American Statistician, August 1975, Vol. 29, No. 3

On the Monty Hall Problem

I have received a number of letters commenting on my "Letters to the Editor" in The American Statistician of February, 1975, entitled "A Problem in Probability." Several correspondents claim my answer is incorrect. The basis to my solution is that Monty Hall knows which box contains the keys and when he can open either of two boxes without exposing the keys, he chooses between them at random. An alternative solution to enumerating the mutually exclusive and equally likely outcomes is as follows:

A = event that keys are contained in box B

B = event that contestant chooses box B

C = event that Monty Hall opens box A

Then

P(keys in box B | contestant selects B and Monty opens A)

= P(A | BC) = P(ABC)/P(BC)

=P(C | AB)P(AB)/P(C | B )P(B )

=P(C | AB)P(B | A)P(A)/P(C | B )P(B )

=(1/2)(1/3)(1/3)(1/2)(1/3)

1/3

If the contestant trades his box B for the unopened box on the table, his probability of winning the car is 2/3.

D.L. Ferguson presented a generalization of this problem for the case of n boxes, in which Monty Hall opens p boxes. In this situation, the probability the contestant wins when he switches boxes is (n-1)/[n(n-p-1)].

Benjamin King pointed out the critical assumptions about Monty Hall's behaviour that are necessary to solve the problem, and emphasized that "the prior distribution is not the only part of the probabilistic side of a decision problem that is subjective."

Monty Hall wrote and expressed that he was not "a student of statistics problems" but "the big hole in your argument is that once the first box is seen to be empty, the contestant cannot exchange his box." He continues to say, "Oh and incidentally, after one [box] is seen to be empty, his chances are no longer 50/50 but remain what they were in the first place, one out of three. It just seems to the contestant that one box having been eliminated, he stands a better chance. Not so." I could not have said it better myself.

Steve Selvin

School of Public Health

University of California

Berkley, CA

Monty's Posterior

A response to Steve Selvin's "A Problem in Probability"

Selvin's note solved an interesting problem concerning the well-known TV show 'Let's Make a Deal.' However, his solution via an enumeration approach is confirmed by a more straight-forward procedure as follows. Consider the following events and probabilities:

P(A = Key box in hand) = 1/3

P(B = Key box on table) = 2/3

P(C = Monty opens empty box on table) = 1

Then, revising probabilities in the light on Monty's action yields:

Hence, the probability of the remaining unopened box on the table containing the keys is 2/3, the contestant should switch.

Joseph G. Van Matre

School of Business

University of Alabama in Birmingham

Edited October 20, 2007 by A_Traveller

[A_Traveller]

An article from John Kay which engendered a spirited correspondence.

Most of us are highly likely to get probability wrong

16 August 2005 Financial Times

Why do we find the mathematics of probability so hard? And why this should make us hesitant to trust lawyers or doctors - and even ourselves

The Monty Hall problem is named after the host of a 1970s quiz show, Let’s Make a Deal. The successful contestant chooses from three closed boxes. One contains the keys to a car and the other two a picture of a goat. The choice made, Monty opens one of the other doors to reveal – a goat. He taunts the guest to change the decision. Should the guest switch to the other closed box?

When the solution was published in an American magazine, thousands of readers – including professors of statistics – alleged an error. Paul Erdös, the great mathematician, reputedly died still musing on the Monty Hall problem. But the answer is, indeed, yes: you should change.

This is not the only case where intuition does not correspond to the mathematics of probability. One person in a 1,000 suffers from a rare disease. A friend has just tested positive for this illness and the test gives a correct diagnosis in 99 per cent of cases. How likely is it that your friend has the disease? Not at all likely. In random groups of 1,000 people an average of 10 would display false positives and only one would be correctly diagnosed with the disease. But most people, including most doctors, think otherwise. “The human mind,” said science writer Stephen Jay Gould, “did not evolve to deal with probabilities.”

Last month, the General Medical Council struck off Professor Sir Roy Meadow, the paediatrician, from the medical register. He had given misleading evidence in the criminal prosecution of Sally Clarke, whose two infants died in their cots. When Mrs Clarke was charged with their murder, Sir Roy told the jury that the chances of two successive cot deaths in the one family was “one in 73m”.

But although the disciplinary committee heard evidence from distinguished statisticians, it does not appear that they understood the application of probability theory to such cases any better than Sir Roy. The committee found that he had underestimated the incidence of cot deaths, and that he had not taken account of genetic and environmental factors that mean a household that experiences one cot death is more likely than average to suffer another. But even if you recognise these effects, his key conclusion remains valid. It is unlikely that such an accident would have happened at all. It is very unlikely indeed that such an accident could have happened twice in the same family.

Of course it is unlikely. The events that give rise to criminal cases are always unlikely, otherwise the courts would be unable to deal with the backlog. If Osama bin Laden is ever brought to justice, the question will not be “is it likely that two aircraft hit the World Trade Center on September 11?” – to which the answer is no – but “given that two aircraft did hit the World Trade Center on September 11, is it likely that bin Laden was responsible?” Confusion of these two separate issues has become known as “the prosecutor’s fallacy”.

A cot death in a family increases the probability that there will be another, but a murder in a family may well increase the probability of another murder by even more: wicked parents may continue to be wicked. Sir Roy might have been right to conclude that two cot deaths were more suspicious than one. But the Court of Appeal, releasing Mrs Clarke, was certainly right to have concluded that this statistical evidence could never, on its own, establish guilt beyond reasonable doubt.

You should not trust doctors, or lawyers, with probabilities; and be very hesitant about trusting yourself. Adversarial legal proceedings are a bad forum for unravelling technical issues. And we cannot expunge collective responsibility for mistakes by excoriating selected individuals.

The business and financial system, more than Bernie Ebbers and Henry Blodget, was to blame for the dotcom boom and bust. Failures in legal processes, rather than over-confident professors, led to the unjust conviction of women such as Sally Clarke. But scapegoating has a long history – at least since Leviticus: “Aaron shall lay both his hands upon the head of the live goat, and confess over him all the iniquities of the children of Israel . . . and the goat shall bear upon him all their iniquities unto a land not inhabited”.[END]

For fellow Brits herein, this show, nor even a Bob Monkhouse version was ever shown in the UK. Noting the point about Paul Erdös herein, it's clearly a problem {whatever you call it} which engages minds.

Regards

Edited October 20, 2007 by A_Traveller

[jstumbo]

An article from John Kay which engendered a spirited correspondence.

Most of us are highly likely to get probability wrong

16 August 2005 Financial Times

Why do we find the mathematics of probability so hard? And why this should make us hesitant to trust lawyers or doctors - and even ourselves

The Monty Hall problem is named after the host of a 1970s quiz show, Let’s Make a Deal. The successful contestant chooses from three closed boxes. One contains the keys to a car and the other two a picture of a goat. The choice made, Monty opens one of the other doors to reveal – a goat. He taunts the guest to change the decision. Should the guest switch to the other closed box?

When the solution was published in an American magazine, thousands of readers – including professors of statistics – alleged an error. Paul Erdös, the great mathematician, reputedly died still musing on the Monty Hall problem. But the answer is, indeed, yes: you should change.

This is not the only case where intuition does not correspond to the mathematics of probability. One person in a 1,000 suffers from a rare disease. A friend has just tested positive for this illness and the test gives a correct diagnosis in 99 per cent of cases. How likely is it that your friend has the disease? Not at all likely. In random groups of 1,000 people an average of 10 would display false positives and only one would be correctly diagnosed with the disease. But most people, including most doctors, think otherwise. “The human mind,” said science writer Stephen Jay Gould, “did not evolve to deal with probabilities.”

Last month, the General Medical Council struck off Professor Sir Roy Meadow, the paediatrician, from the medical register. He had given misleading evidence in the criminal prosecution of Sally Clarke, whose two infants died in their cots. When Mrs Clarke was charged with their murder, Sir Roy told the jury that the chances of two successive cot deaths in the one family was “one in 73m”.

But although the disciplinary committee heard evidence from distinguished statisticians, it does not appear that they understood the application of probability theory to such cases any better than Sir Roy. The committee found that he had underestimated the incidence of cot deaths, and that he had not taken account of genetic and environmental factors that mean a household that experiences one cot death is more likely than average to suffer another. But even if you recognise these effects, his key conclusion remains valid. It is unlikely that such an accident would have happened at all. It is very unlikely indeed that such an accident could have happened twice in the same family.

Of course it is unlikely. The events that give rise to criminal cases are always unlikely, otherwise the courts would be unable to deal with the backlog. If Osama bin Laden is ever brought to justice, the question will not be “is it likely that two aircraft hit the World Trade Center on September 11?” – to which the answer is no – but “given that two aircraft did hit the World Trade Center on September 11, is it likely that bin Laden was responsible?” Confusion of these two separate issues has become known as “the prosecutor’s fallacy”.

A cot death in a family increases the probability that there will be another, but a murder in a family may well increase the probability of another murder by even more: wicked parents may continue to be wicked. Sir Roy might have been right to conclude that two cot deaths were more suspicious than one. But the Court of Appeal, releasing Mrs Clarke, was certainly right to have concluded that this statistical evidence could never, on its own, establish guilt beyond reasonable doubt.

You should not trust doctors, or lawyers, with probabilities; and be very hesitant about trusting yourself. Adversarial legal proceedings are a bad forum for unravelling technical issues. And we cannot expunge collective responsibility for mistakes by excoriating selected individuals.

The business and financial system, more than Bernie Ebbers and Henry Blodget, was to blame for the dotcom boom and bust. Failures in legal processes, rather than over-confident professors, led to the unjust conviction of women such as Sally Clarke. But scapegoating has a long history – at least since Leviticus: “Aaron shall lay both his hands upon the head of the live goat, and confess over him all the iniquities of the children of Israel . . . and the goat shall bear upon him all their iniquities unto a land not inhabited”.[END]

For fellow Brits herein, this show, nor even a Bob Monkhouse version was ever shown in the UK. Noting the point about Paul Erdös herein, it's clearly a problem {whatever you call it} which engages minds.

Regards

So you pick door one. If the odds that the car is behind door 1 is 1/3 and behind door 2 is 1/3 and door 3 is 1/3, then why after showing that door 3 does not contain the car, does door 2 jump up to 2/3 chance of being the car. If door one had just as big as chance to begin with, why does it not jump up to 2/3 chance instead?

[jstumbo]

Isn't this example like saying that if you flip a coin it has a 50:50 chance of being heads. You look at it after flipping and see that it is heads, and then you still say that it only has a 50% chance of being heads, refusing to adjust the percentage chances after knowing more information?

Sure originally the chances of door one having the prize were 1/3 but after you have the additional informaton, it changes the odds. If you were to take a person and have them guess between door one and two after door three had the goat, would they win 2/3 of the time by just guessing different from the person that guessed when there were 3 choices, even though when they guess there are only two choices, door one or door two, one having a car?

I guess it is really a matter of odds vs probability, which are really different things. probability wise, maybe it is 2/3 but odd wise, it is 1/2. If you flipped a coin and it was heads 10 times in a row and then you were going to flip a again, what are the odds that it would be heads vs tails. I would say that it would still be 50:50. But the probability that you could flip a coin 11 times in a row and have it be heads is much smaller than 50:50.

Edited October 20, 2007 by jstumbo