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Post by Guest Mon Apr 08, 2013 2:09 pm

what is the probability of getting a 1 in 100 rolls of a die?

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Post by Guest Mon Apr 08, 2013 2:15 pm

Bhy must you ashk?

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Post by Seva Lamberdar Mon Apr 08, 2013 2:16 pm

Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

are you still using a "die"? why is the plural for "die" not "dies" (like one die, two dies, three dies)?
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Post by Seva Lamberdar Mon Apr 08, 2013 2:19 pm

btw is the answer to your question 1 - (5/6)^100
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Post by MaxEntropy_Man Mon Apr 08, 2013 4:57 pm

Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

to state it as a probability problem you have to tighten your question more. which of the following questions are you asking?

(a) what is the probability in 100 rolls of a die, of getting 1 exactly once?

(b) what is the probability in 100 rolls of a die, of getting 1 at least once?

the answers for (a) and (b) are different.
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Post by Seva Lamberdar Mon Apr 08, 2013 5:01 pm

MaxEntropy_Man wrote:
Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

to state it as a probability problem you have to tighten your question more. which of the following questions are you asking?

(a) what is the probability in 100 rolls of a die, of getting 1 exactly once?

(b) what is the probability in 100 rolls of a die, of getting 1 at least once?

the answers for (a) and (b) are different.

Obviously.
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Post by MaxEntropy_Man Mon Apr 08, 2013 5:06 pm

Seva Lamberdar wrote:
MaxEntropy_Man wrote:
Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

to state it as a probability problem you have to tighten your question more. which of the following questions are you asking?

(a) what is the probability in 100 rolls of a die, of getting 1 exactly once?

(b) what is the probability in 100 rolls of a die, of getting 1 at least once?

the answers for (a) and (b) are different.

Obviously.

what is not obvious is which of the two questions he was asking. the question as he stated it is ambiguous.
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Post by Guest Tue Apr 09, 2013 1:10 am

Vidya Bagchi wrote:Bhy must you ashk?
sevaji once vehemently challenged the correct solution to the monty hall problem. so i want to test what other correct solutions he would like to challenge.
Seva Lamberdar wrote:btw is the answer to your question 1 - (5/6)^100
correct
MaxEntropy_Man wrote:
Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

to state it as a probability problem you have to tighten your question more. which of the following questions are you asking?

(a) what is the probability in 100 rolls of a die, of getting 1 exactly once?

(b) what is the probability in 100 rolls of a die, of getting 1 at least once?

the answers for (a) and (b) are different.
sorry, i meant (b).

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Post by Seva Lamberdar Tue Apr 09, 2013 8:40 am

Huzefa Kapasi wrote:
Vidya Bagchi wrote:Bhy must you ashk?
sevaji once vehemently challenged the correct solution to the monty hall problem. so i want to test what other correct solutions he would like to challenge.
Seva Lamberdar wrote:btw is the answer to your question 1 - (5/6)^100
correct
MaxEntropy_Man wrote:
Huzefa Kapasi wrote:what is the probability of getting a 1 in 100 rolls of a die?

to state it as a probability problem you have to tighten your question more. which of the following questions are you asking?

(a) what is the probability in 100 rolls of a die, of getting 1 exactly once?

(b) what is the probability in 100 rolls of a die, of getting 1 at least once?

the answers for (a) and (b) are different.
sorry, i meant (b).



Now let's have the answer to (a).
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Post by Guest Tue Apr 09, 2013 9:03 am

Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

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Post by MaxEntropy_Man Tue Apr 09, 2013 9:50 am

Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

knowing is different from understanding. google helps in finding out and therefore knowing the answer, but to understand, google alone is insufficient. this difference is gradually being dangerously blurred (IMO) in kids' minds these days.
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Post by Guest Tue Apr 09, 2013 9:52 am

MaxEntropy_Man wrote:google helps in finding out and therefore knowing the answer, but to understand, google alone is insufficient.
scratch whattttttttttt????? what "extra" is required to "understand?" thayir sadam?

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Post by MaxEntropy_Man Tue Apr 09, 2013 10:00 am

Huzefa Kapasi wrote:
MaxEntropy_Man wrote:google helps in finding out and therefore knowing the answer, but to understand, google alone is insufficient.
scratch whattttttttttt????? what "extra" is required to "understand?" thayir sadam?

working out problems successfully without consulting google, making up and solving alternate related problems on their own, and trying to find real world applications.
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Post by Seva Lamberdar Tue Apr 09, 2013 10:48 am

Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

Lol. That simply means I don't accept blindly what is written on the Internet. Btw, how do you know what google says about "monty hall" is correct?
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Post by Guest Tue Apr 09, 2013 10:54 am

Seva Lamberdar wrote:
Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

Lol. That simply means I don't accept blindly what is written on the Internet. Btw, how do you know what google says about "monty hall" is correct?
sevaji, i believe or "know" that the solution show in the wikipedia write up is correct because:

1) it was statistically tested (there are references in the article) and found to be correct;
2) i may be wrong but carvaka had simulated it too on his worksheet and established that it is right;
3) the solution follows the laws of probability and thus HAS to be right regardless of what your instincts say.

anyway, in the face of 1 and 2, it would be foolish to continue to debunk the solution.

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Post by Seva Lamberdar Tue Apr 09, 2013 11:22 am

Huzefa Kapasi wrote:
Seva Lamberdar wrote:
Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

Lol. That simply means I don't accept blindly what is written on the Internet. Btw, how do you know what google says about "monty hall" is correct?
sevaji, i believe or "know" that the solution show in the wikipedia write up is correct because:

1) it was statistically tested (there are references in the article) and found to be correct;
2) i may be wrong but carvaka had simulated it too on his worksheet and established that it is right;
3) the solution follows the laws of probability and thus HAS to be right regardless of what your instincts say.

anyway, in the face of 1 and 2, it would be foolish to continue to debunk the solution.

1) seemed to be contrived ... can't say it was independently tested statistically.

2) writing a computer program (using worsheet etc.) is not a correct statistical simulation. this technique usually helps in justifying what has been said ("proven") already as right or wrong, that's all.

3) there already were assumptions in the demo. regarding the probability of what might or might not be behind the doors before being opened. It was not a completely fair or unbiased situation.
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Post by MaxEntropy_Man Tue Apr 09, 2013 11:33 am

here is the solution i had written down on the sulekha thread which involves no simulation:

this is a bayes theorem problem if we were to assume that the host will
always throw open an empty door. this is an important assumption which
is required to obtain a counter-intuitive result which i suspect was vos
savan't solution since it generated so much incredulity. it's hard to
write symbolic equations here, so instead i'll state the scenarios in
words below. let's assume A has the car and B and C are empty.

case 1 (player chooses A):
in this case, the guest will throw open either C or B; switching is a
losing proposition.

case 2 (player chooses B):
in this case, the guest will throw open C; switching wins.

case 3 (player chooses C):
in this case, the guest will throw open B; switching wins again.

thus switching wins in 2 out of 3 possible cases. so the probability of
winning upon switching, conditioned upon being shown an empty door is
2/3.

it is less wordy if baye's theorem is used. i am quite certain i have
the right answer.
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Post by Guest Tue Apr 09, 2013 1:14 pm

Seva Lamberdar wrote:
Huzefa Kapasi wrote:
Seva Lamberdar wrote:
Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

Lol. That simply means I don't accept blindly what is written on the Internet. Btw, how do you know what google says about "monty hall" is correct?
sevaji, i believe or "know" that the solution show in the wikipedia write up is correct because:

1) it was statistically tested (there are references in the article) and found to be correct;
2) i may be wrong but carvaka had simulated it too on his worksheet and established that it is right;
3) the solution follows the laws of probability and thus HAS to be right regardless of what your instincts say.

anyway, in the face of 1 and 2, it would be foolish to continue to debunk the solution.

1) seemed to be contrived ... can't say it was independently tested statistically.

2) writing a computer program (using worsheet etc.) is not a correct statistical simulation. this technique usually helps in justifying what has been said ("proven") already as right or wrong, that's all.

3) there already were assumptions in the demo. regarding the probability of what might or might not be behind the doors before being opened. It was not a completely fair or unbiased situation.
you are so uff and obsessed with shiva lingam.

read max's post above.

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Post by Seva Lamberdar Tue Apr 09, 2013 2:28 pm

Huzefa Kapasi wrote:

you are so uff and obsessed with shiva lingam.

read max's post above.

What about it .... what if the game-host always shows the empty "door" first, what will then be the probability of a prize behind 2nd or 3rd door?
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Post by MaxEntropy_Man Tue Apr 09, 2013 2:33 pm

Seva Lamberdar wrote:
Huzefa Kapasi wrote:

you are so uff and obsessed with shiva lingam.

read max's post above.

What about it .... what if the game-host always shows the empty "door" first, what will then be the probability of a prize behind 2nd or 3rd door?

that was not the original question. i.e. the original question was NOT to calculate the probability of a prize behind the 2nd or 3rd door. the question was what is the probability that after making a choice, and that the host is always going to throw open an empty door, switching produces a win. every single word in that question is important, because the question you ask is not the question that was originally posed.
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Post by Idéfix Tue Apr 09, 2013 2:45 pm

Haha, that certainly reminds me of old times!

http://indiapulse.sulekha.com/forums/games_why-the-game-show-puzzle-is-puzzling-at-first-69847

The correct answer to the game show puzzle is counter-intuitive. This is because of two reasons: 1. human psychology / behavior, and 2. conditional probability

1. Human psychology / behavior: The host is a person. When we think of people making decisions, we intuitively look for their motives and then deduce the decisions they might make from their motives. We assume that the host is trying to "win" the game, or to be precise, that the host is trying to prevent the player from winning the car. If the host is indeed doing this, switching does not pay. If you initially picked an empty door, the host can open the door with the car, and you immediately lose. If you initially picked the car, the host will open an empty door and give you the option to switch. In this instance, you should not switch. So the dominant strategy (the strategy that wins more often than others) is to not switch. However, vos Savant and other who responded to FF's question here made the assumption that the host is not trying to actively prevent the player from winning. Under this assumption, it does make sense to switch.

2. Conditional probability: Imagine a person who just tuned into the program after the empty door has been opened by the host. If this person now picks one of the two remaining doors, the probability that he picks the car is indeed 1/2. He has no prior information about what happened. So why is the probability that the player will win if he switches 2/3? The key thing here is the information that the player has. The host knows where the car is. The host uses that knowledge to decide which door to open (he always opens an empty door.) Indirectly, the player has the information that the door that the host will open will CERTAINLY be empty. Imagine a different scenario. If the host was completely unaware of where the car is. He opens one of the two doors not picked by the player. Some times it has a car; at other times it doesn't (the probability that there is a car behind the door the host opens: 1/3.) Once the door has been opened thusly, if there happens to be no car behind that door, the probability the car is behind each of the remaining doors is simply 1/2. Because the host did NOT use fore-knowledge of where the car is to decide which door to open, the odds are even. However, in the game show puzzle, the host does use his knowledge of where the car is. Hence the changed odds. Counter-intuitive results occur in situations where the simplified rules (aka heuristics) we use for everyday decision-making are not sophisticated enough to deal with a nuanced problem. The game show puzzle is one such nuanced problem.

Addendum:

There is a third reason this puzzle trips up people. This reason is very specific to a small set of individuals, best represented on CH by Seva. This reason is:

3. Ego: The person solving the puzzle is prone to the two traps I laid out above. Once the person falls into either or both of the traps, there are two choices: acknowledge that one has been tripped up, or get sunk deeper into the trap and keep deluding oneself that one is not trapped. The first choice is a difficult one to make, since it needs one to acknowledge that one can possibly make mistakes. If one's ego is such that this admission is especially difficult to make, the second option seems more attractive. In this rare, but especially entertaining scenario, the person solving the puzzle behaves like the mythical cat that surreptitiously drinks milk with its eyes closed, thinking that if it closes its eyes, the rest of the world can't see it drinking the milk.
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Post by Guest Tue Apr 09, 2013 2:55 pm

Idéfix wrote:Haha, that certainly reminds me of old times!

http://indiapulse.sulekha.com/forums/games_why-the-game-show-puzzle-is-puzzling-at-first-69847

The correct answer to the game show puzzle is counter-intuitive. This is because of two reasons: 1. human psychology / behavior, and 2. conditional probability

1. Human psychology / behavior: The host is a person. When we think of people making decisions, we intuitively look for their motives and then deduce the decisions they might make from their motives. We assume that the host is trying to "win" the game, or to be precise, that the host is trying to prevent the player from winning the car. If the host is indeed doing this, switching does not pay. If you initially picked an empty door, the host can open the door with the car, and you immediately lose. If you initially picked the car, the host will open an empty door and give you the option to switch. In this instance, you should not switch. So the dominant strategy (the strategy that wins more often than others) is to not switch. However, vos Savant and other who responded to FF's question here made the assumption that the host is not trying to actively prevent the player from winning. Under this assumption, it does make sense to switch.

2. Conditional probability: Imagine a person who just tuned into the program after the empty door has been opened by the host. If this person now picks one of the two remaining doors, the probability that he picks the car is indeed 1/2. He has no prior information about what happened. So why is the probability that the player will win if he switches 2/3? The key thing here is the information that the player has. The host knows where the car is. The host uses that knowledge to decide which door to open (he always opens an empty door.) Indirectly, the player has the information that the door that the host will open will CERTAINLY be empty. Imagine a different scenario. If the host was completely unaware of where the car is. He opens one of the two doors not picked by the player. Some times it has a car; at other times it doesn't (the probability that there is a car behind the door the host opens: 1/3.) Once the door has been opened thusly, if there happens to be no car behind that door, the probability the car is behind each of the remaining doors is simply 1/2. Because the host did NOT use fore-knowledge of where the car is to decide which door to open, the odds are even. However, in the game show puzzle, the host does use his knowledge of where the car is. Hence the changed odds. Counter-intuitive results occur in situations where the simplified rules (aka heuristics) we use for everyday decision-making are not sophisticated enough to deal with a nuanced problem. The game show puzzle is one such nuanced problem.

Addendum:

There is a third reason this puzzle trips up people. This reason is very specific to a small set of individuals, best represented on CH by Seva. This reason is:

3. Ego: The person solving the puzzle is prone to the two traps I laid out above. Once the person falls into either or both of the traps, there are two choices: acknowledge that one has been tripped up, or get sunk deeper into the trap and keep deluding oneself that one is not trapped. The first choice is a difficult one to make, since it needs one to acknowledge that one can possibly make mistakes. If one's ego is such that this admission is especially difficult to make, the second option seems more attractive. In this rare, but especially entertaining scenario, the person solving the puzzle behaves like the mythical cat that surreptitiously drinks milk with its eyes closed, thinking that if it closes its eyes, the rest of the world can't see it drinking the milk.

The Main Bore strikes again.

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Post by Seva Lamberdar Tue Apr 09, 2013 4:12 pm

Idéfix wrote:Haha, that certainly reminds me of old times!

http://indiapulse.sulekha.com/forums/games_why-the-game-show-puzzle-is-puzzling-at-first-69847

The correct answer to the game show puzzle is counter-intuitive. This is because of two reasons: 1. human psychology / behavior, and 2. conditional probability

1. Human psychology / behavior: The host is a person. When we think of people making decisions, we intuitively look for their motives and then deduce the decisions they might make from their motives. We assume that the host is trying to "win" the game, or to be precise, that the host is trying to prevent the player from winning the car. If the host is indeed doing this, switching does not pay. If you initially picked an empty door, the host can open the door with the car, and you immediately lose. If you initially picked the car, the host will open an empty door and give you the option to switch. In this instance, you should not switch. So the dominant strategy (the strategy that wins more often than others) is to not switch. However, vos Savant and other who responded to FF's question here made the assumption that the host is not trying to actively prevent the player from winning. Under this assumption, it does make sense to switch.

2. Conditional probability: Imagine a person who just tuned into the program after the empty door has been opened by the host. If this person now picks one of the two remaining doors, the probability that he picks the car is indeed 1/2. He has no prior information about what happened. So why is the probability that the player will win if he switches 2/3? The key thing here is the information that the player has. The host knows where the car is. The host uses that knowledge to decide which door to open (he always opens an empty door.) Indirectly, the player has the information that the door that the host will open will CERTAINLY be empty. Imagine a different scenario. If the host was completely unaware of where the car is. He opens one of the two doors not picked by the player. Some times it has a car; at other times it doesn't (the probability that there is a car behind the door the host opens: 1/3.) Once the door has been opened thusly, if there happens to be no car behind that door, the probability the car is behind each of the remaining doors is simply 1/2. Because the host did NOT use fore-knowledge of where the car is to decide which door to open, the odds are even. However, in the game show puzzle, the host does use his knowledge of where the car is. Hence the changed odds. Counter-intuitive results occur in situations where the simplified rules (aka heuristics) we use for everyday decision-making are not sophisticated enough to deal with a nuanced problem. The game show puzzle is one such nuanced problem.

Addendum:

There is a third reason this puzzle trips up people. This reason is very specific to a small set of individuals, best represented on CH by Seva. This reason is:

3. Ego: The person solving the puzzle is prone to the two traps I laid out above. Once the person falls into either or both of the traps, there are two choices: acknowledge that one has been tripped up, or get sunk deeper into the trap and keep deluding oneself that one is not trapped. The first choice is a difficult one to make, since it needs one to acknowledge that one can possibly make mistakes. If one's ego is such that this admission is especially difficult to make, the second option seems more attractive. In this rare, but especially entertaining scenario, the person solving the puzzle behaves like the mythical cat that surreptitiously drinks milk with its eyes closed, thinking that if it closes its eyes, the rest of the world can't see it drinking the milk.

LOL. So, when you left Sulekha, she let you take your favorite posts with you?
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Post by Guest Wed Apr 10, 2013 1:29 am

mishtake (corrected by my older).
Huzefa Kapasi wrote:
Seva Lamberdar wrote:

Now let's have the answer to (a).
google helps: combin(100,1)*(1/6)*(5/6)^99 OR combin(100,1) * answer to (b)

evidently google does not help you when it comes to monty hall. Razz

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Post by Seva Lamberdar Wed Apr 10, 2013 7:42 am

Seva Lamberdar wrote:
Idéfix wrote:Haha, that certainly reminds me of old times!

http://indiapulse.sulekha.com/forums/games_why-the-game-show-puzzle-is-puzzling-at-first-69847

The correct answer to the game show puzzle is counter-intuitive. This is because of two reasons: 1. human psychology / behavior, and 2. conditional probability

1. Human psychology / behavior: The host is a person. When we think of people making decisions, we intuitively look for their motives and then deduce the decisions they might make from their motives. We assume that the host is trying to "win" the game, or to be precise, that the host is trying to prevent the player from winning the car. If the host is indeed doing this, switching does not pay. If you initially picked an empty door, the host can open the door with the car, and you immediately lose. If you initially picked the car, the host will open an empty door and give you the option to switch. In this instance, you should not switch. So the dominant strategy (the strategy that wins more often than others) is to not switch. However, vos Savant and other who responded to FF's question here made the assumption that the host is not trying to actively prevent the player from winning. Under this assumption, it does make sense to switch.

2. Conditional probability: Imagine a person who just tuned into the program after the empty door has been opened by the host. If this person now picks one of the two remaining doors, the probability that he picks the car is indeed 1/2. He has no prior information about what happened. So why is the probability that the player will win if he switches 2/3? The key thing here is the information that the player has. The host knows where the car is. The host uses that knowledge to decide which door to open (he always opens an empty door.) Indirectly, the player has the information that the door that the host will open will CERTAINLY be empty. Imagine a different scenario. If the host was completely unaware of where the car is. He opens one of the two doors not picked by the player. Some times it has a car; at other times it doesn't (the probability that there is a car behind the door the host opens: 1/3.) Once the door has been opened thusly, if there happens to be no car behind that door, the probability the car is behind each of the remaining doors is simply 1/2. Because the host did NOT use fore-knowledge of where the car is to decide which door to open, the odds are even. However, in the game show puzzle, the host does use his knowledge of where the car is. Hence the changed odds. Counter-intuitive results occur in situations where the simplified rules (aka heuristics) we use for everyday decision-making are not sophisticated enough to deal with a nuanced problem. The game show puzzle is one such nuanced problem.

Addendum:

There is a third reason this puzzle trips up people. This reason is very specific to a small set of individuals, best represented on CH by Seva. This reason is:

3. Ego: The person solving the puzzle is prone to the two traps I laid out above. Once the person falls into either or both of the traps, there are two choices: acknowledge that one has been tripped up, or get sunk deeper into the trap and keep deluding oneself that one is not trapped. The first choice is a difficult one to make, since it needs one to acknowledge that one can possibly make mistakes. If one's ego is such that this admission is especially difficult to make, the second option seems more attractive. In this rare, but especially entertaining scenario, the person solving the puzzle behaves like the mythical cat that surreptitiously drinks milk with its eyes closed, thinking that if it closes its eyes, the rest of the world can't see it drinking the milk.

LOL. So, when you left Sulekha, she let you take your favorite posts with you?

Anyway, here is the link to the solution according to me,

https://such.forumotion.com/t12295-monty-hall-problem-revisited
Seva Lamberdar
Seva Lamberdar

Posts : 6572
Join date : 2012-11-29

https://docs.google.com/document/d/1bYp0igbxHcmg1G1J-qw0VUBSn7Fu

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