Ask Marilyn
December 25th, 2011 at 9:40:59 AM
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This post refers to the Ask Marilyn column on 12-25-11. Please follow the link to the question and answer.
Either I misunderstand the question or Marilyn does. I interpret the question to be what is the likelihood any one employee is chosen at least once over the course of a year.
My answer to that would be 1-(1-.25)^4 = 68.36%. In other words the probability of escaping four drug tests is .75*.75*.75*.75. So the chances of getting picked at least once is 1-.75*.75*.75*.75.
As an aside, if the probability of being chosen is p, and the number of tests is 1/p, as p approaches zero the probability of being selected at least once approaches (e-1)/e.
This is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question.
How do you interpret the question being asked?
Either I misunderstand the question or Marilyn does. I interpret the question to be what is the likelihood any one employee is chosen at least once over the course of a year.
My answer to that would be 1-(1-.25)^4 = 68.36%. In other words the probability of escaping four drug tests is .75*.75*.75*.75. So the chances of getting picked at least once is 1-.75*.75*.75*.75.
As an aside, if the probability of being chosen is p, and the number of tests is 1/p, as p approaches zero the probability of being selected at least once approaches (e-1)/e.
This is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question.
How do you interpret the question being asked?
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 25th, 2011 at 9:46:55 AM
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I would say that your interpretation makes the most sense in response to the reader's question... although I think you may have also had a typo yourself when you stated "This is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question", as these seem to be separate issues unless i am mistaken. If she were interpreting the question as "what are the chances that an individual is chosen in EACH INDIVIDUAL random drug test", then 25% would seem to be accurate, but as I believe the question was intended, I'd agree with your figures.
Merry Christmas to all.
Merry Christmas to all.
December 25th, 2011 at 10:01:39 AM
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Quote: WizardHow do you interpret the question being asked?
I think one of her associates filled in and wrote the Christmas column. It seems like a really stupid answer, and is not characteristic of her. I don't see any other way of interpreting the question except your way. I'll bet she gets a ton of mail.
It is already being referred to as the infamous Ask Marilyn Christmas column on this forum.
December 25th, 2011 at 10:22:06 AM
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I am going to vote with Wiz on this one. Even without doing the math you can see that you have a greater than 25% chance at being selected. Her answer would be similar to saying "what are the chances of guessing a coin-flip right over 2 flips?" and an answer of "50%." This is first level statistics stuff.
All animals are equal, but some are more equal than others
December 25th, 2011 at 10:53:38 AM
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Wow- I would consider her answer a fireable offense. To make an error on such a simple question when you tout yourself as an expert....
December 25th, 2011 at 10:59:11 AM
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Of course, she's wrong. I wonder if she is humble enough to admit it.
As I recall, Statman had a special fondness of Marylin, and I'm pretty sure that he would even agree that she is wrong.
As I recall, Statman had a special fondness of Marylin, and I'm pretty sure that he would even agree that she is wrong.
I heart Crystal Math.
December 25th, 2011 at 11:20:27 AM
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I, too, agree with the Wizard.
I also have disagreed with Marilyn multiple times, and I even pick on things other than her logic and explanations. Back in November 2007, she wrote about a problem in which the key was related to the Hawaiian alphabet. She referred to Hawaii as "our westernmost state." I took issue with that, but, of course, I never got a reply to my email.
I also have disagreed with Marilyn multiple times, and I even pick on things other than her logic and explanations. Back in November 2007, she wrote about a problem in which the key was related to the Hawaiian alphabet. She referred to Hawaii as "our westernmost state." I took issue with that, but, of course, I never got a reply to my email.
December 25th, 2011 at 11:36:37 AM
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Quote: DocShe referred to Hawaii as "our westernmost state." I took issue with that, but, of course, I never got a reply to my email.
Nice catch! I once wrote to Marilyn about something by postal mail, enclosing a SASE, and didn't get a reply either.
In the unlikely event Marilyn or anyone on her staff should read this, I volunteer to proofread any future columns for free.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 25th, 2011 at 12:09:53 PM
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I suggested she refer to Hawaii as our "southernmost" state. I am such a nerd on these things that I view Alaska as not only our westernmost and northernmost state, but also our easternmost state.Quote: WizardNice catch!
December 25th, 2011 at 2:46:46 PM
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I wonder if she is a fraud. It's a stupid question to get wrong. I still think she had a staffer write the column for her while she vacations in the islands.
December 25th, 2011 at 3:52:16 PM
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Quote: DocI suggested she refer to Hawaii as our "southernmost" state. I am such a nerd on these things that I view Alaska as not only our westernmost and northernmost state, but also our easternmost state.
I would disagree about easternmost, since it doesn't cross the International Date Line. However, I'm open to your argument why you view it as the easternmost. Also, I challenge you to a game of geography trivia your next visit here. I have a Trivial Pursuit game with said category, and no, I haven't memorized the answers.
Quote: pacomartinI wonder if she is a fraud. It's a stupid question to get wrong. I still think she had a staffer write the column for her while she vacations in the islands.
That is putting it a bit strong. However, that last column not only was a bad answer but it also didn't seem like her usual kindergarten-teacher style. The Christmas Break excuse is hard to buy, however. She is fully capable of writing columns a long time in advance. She probably just had a lot on her mind. I certainly have blown it myself more than once. For example, in my last SWD.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 25th, 2011 at 6:34:03 PM
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Quote: WizardThat is putting it a bit strong. However, that last column not only was a bad answer but it also didn't seem like her usual kindergarten-teacher style.
Perhaps. The columns are usually quite accurate. To all of a sudden go from such accuracy to such a bad error makes it seem as if her normal mathematics person was sick.
But I've seen some really bizarre things. I remember going to a meeting with a Deputy Assistant Secretary of the Navy which despite the Deputy Assistant is a very high ranking official in the well over 300,000 man Navy. She kept talking about our SONAR system, but she kept saying RADAR. Since she said it 3 or 4 times it didn't seem to be a mistake. I was stunned that someone that was that high of a rank didn't know what seemed like virtually street knowledge. It was pointed out to me that none of the Captains in the room corrected her, so that I shouldn't either. I felt that it was a little like having your fly down, and no one saying anything to you until you went home at the end of the day.
Of course, one wonders about the Guam will tip over comment as well.
December 25th, 2011 at 6:54:43 PM
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Quote: pacomartinI was stunned that someone that was that high of a rank didn't know what seemed like virtually street knowledge.
Oh, I can quote the sum total of Obama's knowledge on economics:
Quote:
It's a common state of affairs.
Donald Trump is a fucking criminal
December 25th, 2011 at 7:00:44 PM
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Quote: pacomartinOf course, one wonders about the Guam will tip over comment as well.
Ah, the good ol' U S of A. If I didn't laugh at stuff like this I'd have to cry.
This is getting a bit off topic but have a look at this Ali G interview of Pat Buchanan. If you're short on time, fast forward to the 2:30 point and focus on the confusion between the acronyms WMD and BLT. I've always wondered if Buchanan was confused about what BLT stood for or was just going along with the gag. The improvisation on Cohen's part with the mustard gas comment was brilliant.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 25th, 2011 at 7:23:46 PM
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Stupidity seems to be going around.
How long did I wait for Nareed's Obama quote to "load"?
How about we don't worry about it, OK? ><
How long did I wait for Nareed's Obama quote to "load"?
How about we don't worry about it, OK? ><
The opinions of this moderator are for entertainment purposes only.
December 25th, 2011 at 7:38:41 PM
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Quote: WizardIf you're short on time, fast forward to the 2:30 point and focus on the confusion between the acronyms WMD and BLT. I've always wondered if Buchanan was confused about what BLT stood for or was just going along with the gag. The improvisation on Cohen's part with the mustard gas comment was brilliant.
I think clearly there is a point when Buchanan understands that the interview is a total act. By the end when they are talking about sandwiches and bumping fists. There is no specific time where his face changes and he clearly starts joking around, but I think he figured it out pretty quickly.
But working for the military, you do think the acronym overload is just absurd. A lot of times, I think people end up repeating them, so I think it is very possible that the first time Buchanan didn't catch on that BLT was a joke.
I do remember a security officer started screaming about TPI one day. Finally I had to ask what TPI was since it looked like I was going to be punished. TPI means "two person integrity". Of all the stupid acronyms I thought that was one of the dumbest I had ever heard. Why she couldn't say, "you can't be in the room alone", was totally beyond me.
=====================
The recent story about Enrique Pena Nieto (the lead candidate for President of Mexico in the elections in July) stumbling when asked the softball question to name three books that have influenced you at a major book fair in Guadalajara, got him more worldwide press than almost anything he has done in the last two years.
December 25th, 2011 at 8:13:02 PM
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Quote: NareedHey, I spared you the expense of buying the book.
Old joke. I've seen "Everything men know about women" about 25 years ago, which was also totally blank. In my case, I must admit, it was right.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
December 26th, 2011 at 8:40:13 AM
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Quote: WizardI would disagree about easternmost, since it doesn't cross the International Date Line. However, I'm open to your argument why you view it as the easternmost. Also, I challenge you to a game of geography trivia your next visit here. I have a Trivial Pursuit game with said category, and no, I haven't memorized the answers.Quote: DocI suggested she refer to Hawaii as our "southernmost" state. I am such a nerd on these things that I view Alaska as not only our westernmost and northernmost state, but also our easternmost state.
No, Alaska does not cross the International Date Line, specifically because that "line" is deliberately crooked in order to avoid land masses/groupings. As a crooked line, it isn't a reasonable guide as to how far east/west something extends. Alaska does indeed cross the 180th meridian and extends into the eastern hemisphere (or perhaps extends from the eastern hemisphere into the western). Thus, a few of the Aleutian islands are among the farthest east land bodies on the planet. That's why I consider Alaska our easternmost state, even though I admit that it is a quirky perspective.
In my 2007 note to Marilyn, I allowed that she might have been thinking of westernmost in terms of center of mass, but I pointed out that that perspective would suggest that New Hampshire and Rhode Island are farther east than Massachusetts, while most would consider Cape Cod to represent the important factor.
I think I would have to pass on any kind of geography competition, partly because when I studied the topic in elementary school we didn't study the full breadth of it at all, only countries, capitals, rivers, mountain ranges, and such. In 6th grade, we learned the names and capitals of all of the countries in the world. While most of the rivers and mountains haven't changed much, the countries and cities have changed a bunch. It seems that most of the African countries are different from what I studied -- anyone remember the Belgian Congo? French Equatorial Africa? Spanish Saharah? And I still think of India as having a big city named Bombay. Even if I remembered everything I ever studied in geography class (which I certainly don't after all these years), I'd be lost in a geography competition today. I have a failing memory of obsolete facts.
December 26th, 2011 at 10:11:10 AM
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Quote: DocNo, Alaska does not cross the International Date Line, specifically because that "line" is deliberately crooked in order to avoid land masses/groupings. As a crooked line, it isn't a reasonable guide as to how far east/west something extends. Alaska does indeed cross the 180th meridian and extends into the eastern hemisphere (or perhaps extends from the eastern hemisphere into the western). Thus, a few of the Aleutian islands are among the farthest east land bodies on the planet. That's why I consider Alaska our easternmost state, even though I admit that it is a quirky perspective.
Very quirky indeed, and the kind of answer that could be looked upon as intended to stir debate.
And I feel incorrect.
Lines of longitude do not have a definitive "beginning and end." While Lattitude does end at the north and south poles and those poles are a definitive "end" since the earth spins on an axis, longitude could have started anywhere. Where it does start is Prime Merridian, and that line was arbitrarily set thru the living room og the guy who set the whole thing up.
If you want what is IMHO a better and more correct definition for "furthest east/west" states you need to look at the geographic center and then go east and west from there. With AK/HI included as one mass this would put that center probably somewhere in CA, with eastermost out on Cape Cod or Long Island and westernmost at either HI or an Alleutian Island.
Crooked as it is, the Date Line seperates east and west even though the westernmost part of the eastern side is east of the easternmost part of the westernmost side and the western side is the eastern hemisphere and the eastern side is the western hemisphere.
Got all that?
(Yes, that is what explaining craps does to a person's mind.)
All animals are equal, but some are more equal than others
December 26th, 2011 at 10:25:06 AM
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Quote: WizardI've seen "Everything men know about women" about 25 years ago, which was also totally blank. In my case, I must admit, it was right.
They want a handsome, nice, smart guy, but women don't know how Venn diagrams work.
Women also want risk takers who are always available. make it look effortless and always succeed. To be fair that is exactly what men want, but they know that's why they make comic book movies.
January 15th, 2019 at 3:30:58 PM
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Quote: WizardThis is by far the first time I have taken issue with Marilyn's responses. She really stirred up the pot with a bad answer to the Monty Hall question.
What is the Wizard's current position on the Monty Hall problem? She really did stir up a furor with her answer at the time but today every reference authority on the question gives her answer as the correct one. Here is the problem:
On the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.
Here is my favorite solution. We assume that Monty offers the switch whether or not she has chosen correctly.
When she makes her choice the probability is 1/3 that she is right and 2/3 that she is wrong.
If she stays with her original choice she wins if her choice was right p = 1/3
If she switches she wins if her original choice was wrong p = 2/3
She should switch!
"I am not concerned that someone does not know of me; I am concerned that I do not know of him" - Confucius
January 15th, 2019 at 3:47:50 PM
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Quote: shoshone
When she makes her choice the probability is 1/3 that she is right and 2/3 that she is wrong.
If she stays with her original choice she wins if her choice was right p = 1/3
If she switches she wins if her original choice was wrong p = 2/3
She should switch!
My problem here is if she switches or not, her probability is still 1/2. She still has 2 choices. Equal probability either way.
All animals are equal, but some are more equal than others
January 15th, 2019 at 4:07:06 PM
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Quote: shoshoneOn the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.
This vague wording is exactly what was wrong with Marilyn's many columns on the topic. It must be clearly stated what Monty's behavior is.
If he didn't know where the car was and opened a door at random, then the odds the player's door has the car is 1/2.
If he does know where the car is and always opens a door with a goat after the player chooses, then the odds the player's door has the car is 1/3.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 15th, 2019 at 5:17:12 PM
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While I agree with you, even with the vague wording the answer to the question is clear. They player should certainly switch doors. At worst, the player is no worse off, and at best the player just doubled his chances of winning.Quote: WizardQuote: shoshoneOn the show Let's Make a Deal host Monty Hall gives the contestant a choice of three doors. Behind one is an automobile and behind two are goats. She gets to keep whatever is behind the door she chooses. She picks a door. Monty opens one of the other doors and show a goat. Should she stay with her original selection or should she switch? Most of the write-ins said it didn't matter.
This vague wording is exactly what was wrong with Marilyn's many columns on the topic. It must be clearly stated what Monty's behavior is.
If he didn't know where the car was and opened a door at random, then the odds the player's door has the car is 1/2.
If he does know where the car is and always opens a door with a goat after the player chooses, then the odds the player's door has the car is 1/3.
WWBD? (What would Bayes do?)
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 16th, 2019 at 4:59:18 AM
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Never assume.Quote: shoshone... We assume that Monty offers the switch whether or not she has chosen correctly. ...
Monty doesn’t always offer the switch, and he himself has said that he would often offer that option based upon his opinion of the contestant - and that included both the second chance to win the prize as well as the second chance to get zonked.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
January 16th, 2019 at 8:09:22 AM
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Quote: unJon] While I agree with you, even with the vague wording the answer to the question is clear. They player should certainly switch doors. At worst, the player is no worse off, and at best the player just doubled his chances of winning.
WWBD? (What would Bayes do?)
What if the host knew where the car was and planned to only open another door if you picked it, thus tricking Bayesians into switching.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 16th, 2019 at 8:12:29 AM
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Quote: DJTeddyBearMonty doesn’t always offer the switch, and he himself has said that he would often offer that option based upon his opinion of the contestant - and that included both the second chance to win the prize as well as the second chance to get zonked.
I've watched old shows on YouTube and he didn't offer a switch. However, as I recall, he always opened the best door last. Thus, it didn't reveal any pertinent information when he opened one of the lower value doors first. Your chances of winning the best prize were still 1/3 at that point.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 16th, 2019 at 10:22:24 AM
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Quote: WizardI've watched old shows on YouTube and he didn't offer a switch. However, as I recall, he always opened the best door last. Thus, it didn't reveal any pertinent information when he opened one of the lower value doors first. Your chances of winning the best prize were still 1/3 at that point.
It would be interesting to see the total number of times switching was offered, and how many of those were, "Contestant initially picked the big prize." I doesn't sound like it will be 1/3, so maybe the contestant's post Monty's offer action needs to based on more than the revised probability of the offer to switch. Is there a "tell" when Monty wants you to win?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 16th, 2019 at 10:59:58 AM
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I watched a ton of LMaD back in the day, and I don't recall any game on the show that mirrored the "Monty Hall Problem." I'm guessing the "MHP" is strictly a hypothetical problem, but put in the context of LMaD.
The "Big Deal of the Day" was where the two contestants who won the most and were willing to trade it all away each picked one of the three doors/curtains. Once the contestant selected their doors, the doors were always revealed from lowest value to highest value, regardless of who picked what. The contestants were not allowed to switch their picks.
The "Big Deal of the Day" was where the two contestants who won the most and were willing to trade it all away each picked one of the three doors/curtains. Once the contestant selected their doors, the doors were always revealed from lowest value to highest value, regardless of who picked what. The contestants were not allowed to switch their picks.
"Dealer has 'rock'... Pay 'paper!'"
January 16th, 2019 at 11:31:15 AM
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Fair. It’s like the old answer to Pascal’s wager.Quote: WizardWhat if the host knew where the car was and planned to only open another door if you picked it, thus tricking Bayesians into switching.
The race is not always to the swift, nor the battle to the strong; but that is the way to bet.
January 17th, 2019 at 11:09:44 AM
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Quote: DJTeddyBearNever assume.
Monty doesn’t always offer the switch, and he himself has said that he would often offer that option based upon his opinion of the contestant - and that included both the second chance to win the prize as well as the second chance to get zonked.
Since you frequently respond to math postings with "I don't understand the math but..." I conclude that you are not a mathematician, so let me explain:
In analyzing real-life situations mathematicians frequently employ mathematical models which may not perfectly model the situation but which are easy to solve or manipulate. They would rather have an imperfect model that is easy to solve than a precise model that is impossible to solve.
The Monty Hall Problem is just a mathematical problem and does not accurately represent the way Monty ran his show. To make it solvable one stipulates the following conditions:
1. Monty knows which door the car is behind.
2. Monty offers the switch whether the contestant has chosen correctly or not.
Only with these conditions is the problem solvable.
I get the impression that the Wizard still feels that Marilyn's answer was wrong. Well, he is in good company. When Marilyn published her solution she received a flood of letters from people with Ph. D.s and on academic letterheads telling her that she was wrong and begging her to recant. All of these people since have come over to her side.
Marilyn is too modest to present herself as having the world's highest I. Q. Her publisher does that. I used to belong to a high-IQ society (Mensa) and discovered that having a high IQ doesn't prevent some people from saying or doing stupid things. My favorite Marilyn stupidities are:
Q. I bought some stock and it has gone down. What should I do?
A. You have a loss only if you sell.
and
Q. If lost at sea, how do I find land?
A. Follow the waves, for waves always crash on a shore.
Nevertheless, I think that Marilyn contributes to society.
Last edited by: netzer on Jan 17, 2019
OnceDear is a Dear!
January 17th, 2019 at 11:30:51 AM
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Quote: netzerI get the impression that the Wizard still feels that Marilyn's answer was wrong.
No, I feel she was right for how she interpreted the question. I fault her for not clarifying what the question is asking. I found images of the original question and answer.
Question:
Answer:
You can see the question stated that the host knows what is behind the doors. However, he didn't say why he opened up a goat door or if he did this all the time. Marilyn assumed the host will always reveal a goat after the contestant picks a door. Under this assumption, her answer is correct.
However, many people interpret it like there was a door malfunction, revealing a goat. If that was the case, then there is a 50/50 chance the original door has a goat.
I fault her not for giving a wrong answer, but not clarifying what the question is.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2019 at 12:06:24 PM
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It seems Marilyn describes it like this, with 1/3 probability of each initial choice:
However, isn't it actually like this?:
| Initial Unknown Choice | Monty Reveals | You Swtich To | Result |
|---|---|---|---|
| Car | Goat 1 | Goat 2 | Loss |
| Goat 1 | Goat 2 | Car | Win |
| Goat 2 | Goat 1 | Car | Win |
However, isn't it actually like this?:
| Initial Unknown Choice | Monty Reveals | You Swtich To | Result |
|---|---|---|---|
| Car | Goat 1 | Goat 2 | Loss |
| Car | Goat 2 | Goat 1 | Loss |
| Goat 1 | Goat 2 | Car | Win |
| Goat 2 | Goat 1 | Car | Win |
Last edited by: Ayecarumba on Jan 17, 2019
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 17th, 2019 at 1:45:39 PM
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He never offered to switch DOORS. Doors were only used on the big deal finale and never had a zonk - just 3 prizes of widely varying value. Also, the big deal involved two contestants making a switch unfair.Quote: WizardI've watched old shows on YouTube and he didn't offer a switch.
Unfortunately, the problem is always worded using doors rather than curtains. Monty often - but not always - allowed a switch of the curtains (or boxes, etc.).
You’re right. I’m not a mathemetician per se, but this is simple math and I understand and agree with the Marilyn / math answer.Quote: netzerSince you frequently respond to math postings with "I don't understand the math but..." I conclude that you are not a mathematician...
My point is, when you examine the tv show, you have to realize that Monty (and subsequent hosts) had their own reasons and parameters for occasionally offering the switch which adds to the unpredictability and could make the math invalid.
I invented a few casino games. Info:
http://www.DaveMillerGaming.com/ —————————————————————————————————————
Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
January 17th, 2019 at 1:49:04 PM
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Ayecarumba:
I get your point, but I think Marilyn's table was set up like this:
From this table the contestant wins the car once it he stays and twice if he switches. Also, Marilyn considers the goats to be indistinguishable, so there is no goat1 and goat2.
There are many solutions to this problem. Consider this:
You select a door. Monty gives you the choice of staying with your selection or opening both of the other doors and taking your choice. Isn't that the same proposition as showing you which of the other doors doesn't hide the car and letting you choose the other?
I get your point, but I think Marilyn's table was set up like this:
| Behind door 1 | Behind door 2 | Behind door 3 | Result if staying at door #1 | Result if switching to the door offered |
|---|---|---|---|---|
| Goat | Goat | Car | Wins goat | Wins car |
| Goat | Car | Goat | Wins goat | Wins car |
| Car | Goat | Goat | Wins car | Wins goat |
From this table the contestant wins the car once it he stays and twice if he switches. Also, Marilyn considers the goats to be indistinguishable, so there is no goat1 and goat2.
There are many solutions to this problem. Consider this:
You select a door. Monty gives you the choice of staying with your selection or opening both of the other doors and taking your choice. Isn't that the same proposition as showing you which of the other doors doesn't hide the car and letting you choose the other?
OnceDear is a Dear!
January 17th, 2019 at 3:25:19 PM
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Quote: netzerYou select a door. Monty gives you the choice of staying with your selection or opening both of the other doors and taking your choice. Isn't that the same proposition as showing you which of the other doors doesn't hide the car and letting you choose the other?
Yes, it is.
As to DJ's point, I agree, this shouldn't be called the Monty Hall problem, because it doesn't reflect his behavior on the show. Yes, it was curtains, not doors.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 17th, 2019 at 4:35:04 PM
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Quote: netzerAyecarumba:
I get your point, but I think Marilyn's table was set up like this:
Behind door 1 Behind door 2 Behind door 3 Result if staying at door #1 Result if switching to the door offered Goat Goat Car Wins goat Wins car Goat Car Goat Wins goat Wins car Car Goat Goat Wins car Wins goat
From this table the contestant wins the car once it he stays and twice if he switches. Also, Marilyn considers the goats to be indistinguishable, so there is no goat1 and goat2.
There are many solutions to this problem. Consider this:
You select a door. Monty gives you the choice of staying with your selection or opening both of the other doors and taking your choice. Isn't that the same proposition as showing you which of the other doors doesn't hide the car and letting you choose the other?
Although none of the variables changed (no prizes switched locations), the odds of the initial selection begin correct changed due to Monty sharing information.
I hate to bring this example up, but how is this different than the "Two Dice" problem? (A game where the dealer shakes two dice under a bowl, then peeks under it and tells you, "one of the dice is a "2". What are the odds the other die is also a "2"?
It has been exhaustively explained that the odds remain 1/11, even with the "new" information that one of the dice is a "2". How does the "new" information in the Monty Hall problem change the odds, while the information in the "Two Dice" problem doesn't?
Simplicity is the ultimate sophistication - Leonardo da Vinci
January 17th, 2019 at 5:18:28 PM
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Quote: WizardI agree, this shouldn't be called the Monty Hall problem, because it doesn't reflect his behavior on the show. Yes, it was curtains, not doors.
Whether we like it or not, the name seems to have stuck. It is essentially the same as Martin Gardner's Three Prisoners Problem and is closely related to Bertrand's Box Problem from a century earlier.
Bed time now in South Africa. Good night!
OnceDear is a Dear!
January 19th, 2019 at 8:55:40 AM
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Quote: Wizard
As to DJ's point, I agree, this shouldn't be called the Monty Hall problem, because it doesn't reflect his behavior on the show.
I think this is probably true. I have scanned a number of episodes of the show. He had a many games involving three doors with all sorts of merchandise behind them but I was unable to find a single instance involving two goats and a car. If anyone can find one, please share.
I did find an interview with Monty in which he said that he offered the contestant money instead of a switch.
OnceDear is a Dear!
January 19th, 2019 at 9:10:50 AM
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Quote: netzerI think this is probably true. I have scanned a number of episodes of the show. He had a many games involving three doors with all sorts of merchandise behind them but I was unable to find a single instance involving two goats and a car. If anyone can find one, please share.
I did find an interview with Monty in which he said that he offered the contestant money instead of a switch.
I have telling people this for years, and more often than not, the response was, "Obviously you've never watched the show."
And it wasn't always money; sometimes, it was a box.
Also, do we call it the Wayne Brady problem now?
January 21st, 2019 at 6:03:15 AM
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Quote: WizardAs to DJ's point, I agree, this shouldn't be called the Monty Hall problem, because it doesn't reflect his behavior on the show. Yes, it was curtains, not doors.
This is true of the later shows but the earlier ones used doors.
From my search, listening to Monty's interview, and the comments of others, I believe it would be correct to say that "The Monty Hall Problem" is a mathematical problem modeled on "Let's Make a Deal" but never was actually played on the show.
The remarkable thing is that so many people, even ones with advanced mathematics degrees, insisted on the wrong answer for so long and that there is so much literature on it. There ie even a book:
Rosenhouse, Jason, The Monty Hall Problem, The Remarkable Story of Math's Most Contentuous Brainteaser
It is available for free on the Internet, but I don't want to say publicly how to get it. Otherwise it is available from Amazon for $25.98.
It is Martin Luther King Day in the United States. I personally think that J. Edgar Hoover contracted for his assassination. Here in South Africa we have the converse problem: the assassination of Whites by Blacks.
OnceDear is a Dear!
January 21st, 2019 at 5:27:45 PM
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Quote: netzerThis is true of the later shows but the earlier ones used doors.
From my search, listening to Monty's interview, and the comments of others, I believe it would be correct to say that "The Monty Hall Problem" is a mathematical problem modeled on "Let's Make a Deal" but never was actually played on the show.
The remarkable thing is that so many people, even ones with advanced mathematics degrees, insisted on the wrong answer for so long and that there is so much literature on it.
I still find that many people can't get past the comparison to Let's Make a Deal if you call it the "Monty Hall Problem." Adding your caveats I don't think will help. People get very fixated on titles.
As to the debate, I have said this many times, but it comes down to how you interpret the question. Here again was the original column:
The one asking the question didn't say why the host opened the door. The correct answer hinges on the answer to that question. For the way Marilyn interpreted the question, her answer is right. It doesn't help that Deal or No Deal is a hit show and everybody seems to draw comparisons to that.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 22nd, 2019 at 9:55:13 AM
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Wizard:
Thank you for posting Marilyn's original statement of the problem. You notice she didn't refer to Monty Hall at all, she merely says "Suppose you're on a game show..." so we can't blame her for the name. We should put the blame on Steve Selvin, who proposed it in a letter to The American Statistician in 1975. I tried to put a link here to the web page where Selvin's letter may be read, but your site will not allow external addresses, at least not for me.
Selvin's scene is Monty's show, but there are no doors and no goats, just three boxes, one of which contains the keys to a 1975 Lincoln Continental. Monty gives the contestant his choice of a box and he takes Box B. Monty offers the contestant $100, $200, $500 for the box, but the contestant says no. Monty opens Box A and it's empty. He offers the contestant $1,000 for his box but the contestant refuses and makes a counter proposal: to switch his Box B for Box C.
Selvin stops at this point and analyzes the problem. He concludes that if Monty accepted the switch the contestant would have a 2/3 chance of winning the car instead of 1/3 if he merely opened his box.
I think this is the original statement of the problem in a game show setting. How the doors and goats got into it is a matter for further research.
I should be glad to lend you my copy of the Rosenhouse book. I could send it as an e-mail attachment.
Thank you for posting Marilyn's original statement of the problem. You notice she didn't refer to Monty Hall at all, she merely says "Suppose you're on a game show..." so we can't blame her for the name. We should put the blame on Steve Selvin, who proposed it in a letter to The American Statistician in 1975. I tried to put a link here to the web page where Selvin's letter may be read, but your site will not allow external addresses, at least not for me.
Selvin's scene is Monty's show, but there are no doors and no goats, just three boxes, one of which contains the keys to a 1975 Lincoln Continental. Monty gives the contestant his choice of a box and he takes Box B. Monty offers the contestant $100, $200, $500 for the box, but the contestant says no. Monty opens Box A and it's empty. He offers the contestant $1,000 for his box but the contestant refuses and makes a counter proposal: to switch his Box B for Box C.
Selvin stops at this point and analyzes the problem. He concludes that if Monty accepted the switch the contestant would have a 2/3 chance of winning the car instead of 1/3 if he merely opened his box.
I think this is the original statement of the problem in a game show setting. How the doors and goats got into it is a matter for further research.
I should be glad to lend you my copy of the Rosenhouse book. I could send it as an e-mail attachment.
OnceDear is a Dear!
January 22nd, 2019 at 5:33:43 PM
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Thank you for the offer. Can you send me a private message? New members may not post links, but I can. I would also be happy to borrow the Rosenhouse book. I didn't even know e-books could be lent out.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 22nd, 2019 at 6:08:19 PM
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I think we can stipulate that the host will never open the door that contains the big prize, so the contestant has his choice of two doors or curtains.
Does the host always open a curtain? If so, you don't have to choose from three, you only have to choose from any two. Of the two doors remaining, each is fifty -fifty to have the big prize. The door you picked originally is 50-50 now, and the unchosen door is also 50-50. So either choice you make is as good as the other.
This only works if the host will always open a door after you chose.
I've had many an argument on this but no one has convinced me I'm mistaken.
Does the host always open a curtain? If so, you don't have to choose from three, you only have to choose from any two. Of the two doors remaining, each is fifty -fifty to have the big prize. The door you picked originally is 50-50 now, and the unchosen door is also 50-50. So either choice you make is as good as the other.
This only works if the host will always open a door after you chose.
I've had many an argument on this but no one has convinced me I'm mistaken.
The difference between fiction and reality is that fiction is supposed to make sense.
January 22nd, 2019 at 6:47:15 PM
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If you can't be convinced by logical arguments or some other form of explanation that you are mistaken, grab a friend and do an experiment.
Take 3 cards from a deck of cards, such as an ace and a two and a three.
Have your friend put the cards down in front of you, with your friend knowing which one is the ace.
Pick a face down card. Your friend will turn up one of the other cards, never choosing to turn up the ace.
Then record if the ace was the card you originally picked, or if it was the other face down card on the table.
After a bunch of trials, the number of times your original pick was an ace should approach either one half of the time, or one third of the time.
You can actually do the experiment by yourself. Just shuffle the three cards, lay them out and pick one. Then turn up one of the other cards. If the other card is the ace, turn it back down and turn up the other one.
Take 3 cards from a deck of cards, such as an ace and a two and a three.
Have your friend put the cards down in front of you, with your friend knowing which one is the ace.
Pick a face down card. Your friend will turn up one of the other cards, never choosing to turn up the ace.
Then record if the ace was the card you originally picked, or if it was the other face down card on the table.
After a bunch of trials, the number of times your original pick was an ace should approach either one half of the time, or one third of the time.
You can actually do the experiment by yourself. Just shuffle the three cards, lay them out and pick one. Then turn up one of the other cards. If the other card is the ace, turn it back down and turn up the other one.
January 22nd, 2019 at 7:36:57 PM
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You can also play this Monty knows game.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
January 22nd, 2019 at 10:32:27 PM
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Quote: Dalex64If you can't be convinced by logical arguments or some other form of explanation that you are mistaken, grab a friend and do an experiment.
Take 3 cards from a deck of cards, such as an ace and a two and a three.
Have your friend put the cards down in front of you, with your friend knowing which one is the ace.
Pick a face down card. Your friend will turn up one of the other cards, never choosing to turn up the ace.
Then record if the ace was the card you originally picked, or if it was the other face down card on the table.
After a bunch of trials, the number of times your original pick was an ace should approach either one half of the time, or one third of the time.
You can actually do the experiment by yourself. Just shuffle the three cards, lay them out and pick one. Then turn up one of the other cards. If the other card is the ace, turn it back down and turn up the other one.
But you aren't really picking one of three. No matter which one you originally choose, one of the others is eliminated. Your original choice has a 50-50 chance, just like the unlocked box.
While it is true that the unlocked box has a 1 in 2 shot of having the prize, so does your original pick.
The difference between fiction and reality is that fiction is supposed to make sense.
January 22nd, 2019 at 10:50:11 PM
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Quote: billryanBut you aren't really picking one of three. No matter which one you originally choose, one of the others is eliminated. Your original choice has a 50-50 chance, just like the unlocked box.
While it is true that the unlocked box has a 1 in 2 shot of having the prize, so does your original pick.
Best and simplest way to look at it :
Every time you pick the wrong box originally , and the host opens a second one, the third unopened box always has the prize.
How often do you pick the wrong box originally? 66%
So 66% of the time that third unopened box is the prize.
