Marilyn Vos Savant, listed in the "Guinness Book of World Records" as having the highest IQ (I came in second ) was asked the following. What do you think?

Marilyn: As a lecturer in psychology at Erasmus Medical School in the Netherlands, I use a problem that appeared in your column to show how easily one is misled by intuition:

Say you’re on a game show and given a choice of three doors. Behind one door is a car; behind the other two doors are goats. You choose door #1. The show’s host, who knows what’s behind the doors, opens door #3. A goat appears. The host then asks, “Do you want to choose door #2, instead?” Should you switch? You said, “Yes. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.”

This always amazes my students. But then one of them posed the following problem: Suppose I am taking a multiple-choice test. One question has three choices. I randomly choose A. Then the instructor tells us that C is incorrect. Should I switch to B before turning in my paper?

After you decide, here is her answer.

I suppose it's my maths training, but I found this not really very difficult at all...

Marilyn Von Smartass, one of TrossL's personal heros, has come up before here. There's a website specifically devoted to pointing out her (MANY) errors, something along the lines of Marilyn'sanidiot.com.

OK, absolutely no sweat on the multiple choice answer. It's random and the instructor doesn't know what you've chosen. That aspect of the question is a no-brainer.

BUT! The game show portion? Unless someone can explain it otherwise, I see her answer as being 100% bogus. After the host shows one of the goats, "the first door has a 1/3 chance of winning but the third door has a 2/3 chance"??? Nonsense! Of course the host chose one of the goat doors since he (and no gender slight is intended; 100% of all game show hosts are male [or so it seems] though I don't know why) knows where the car is. Before you chose, each door had a 1/3 chance of winning. Now that one goat is out of the way, each of the remaining two doors has a 1/2 chance.

So where does that ridiculous 2/3 figure come into play? I freely admit that Marilyn "Ain't I Sumthin'!" Vos Savant may be correct and I just don't get it and, if so, I'll just as freely admit it, but that 2 out of 3 chance just doesn't make sense to me.

Yes, I agree, CJ. Ros, some elucidation? No matter how brilliant, I don't think Marilynn explained it clearly.

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100% of all game show hosts are male

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But, the wheel turners are female!

According to my daughter who is interning in a law firm this summer, we really haven't come that far with feminism. While we see a lot more women in law schools, the managing partners, rainmakers, etc. are by and large men.

The 2/3 figure is part of the question - the link Kalleh posted gives the answers by whatsername, or at least that's how I understood it.

She's not agreeing with the 2/3 at all...

It's a bit confusing because the person "speaking" is not the person whose name appears at the front of the paragraph. The bit about the 2/3 is posed by Mr Bonke (brilliant name!) and Marilyn refutes that, although she doesn't specifically mention that the chance is 1/2 after 1 door has been opened.

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Marilyn: As a lecturer in psychology at Erasmus Medical School in the Netherlands, I use a problem that appeared in your column to show how easily one is misled by intuition:

Say you’re on a game show and given a choice of three doors. Behind one door is a car; behind the other two doors are goats. You choose door #1. The show’s host, who knows what’s behind the doors, opens door #3. A goat appears. The host then asks, “Do you want to choose door #2, instead?” Should you switch? You said, “Yes. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.”

This always amazes my students. But then one of them posed the following problem: Suppose I am taking a multiple-choice test. One question has three choices. I randomly choose A. Then the instructor tells us that C is incorrect. Should I switch to B before turning in my paper?

Benno Bonke
Rotterdam

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Benno: It doesn’t matter: You have the same chance either way. The two problems are different. In the game show problem, the host chooses which door to open based on your choice. Say there’s a goat behind doors #1 and #3. If you choose door #1, the host will open door #3. If you choose door #3, the host will open door #1. In the classroom problem, the instructor does not make a statement that an answer is incorrect based on your choice. He isn’t even aware of your choice. Instead, he merely announces to the class that one of the answers is incorrect.

One of the few readers who wrote to agree with my answer was Millard Susman, Professor Emeritus from the Medical School and College of Agricultural and Life Sciences at the University of Wisconsin at Madison. He said, “Probability problems are often subtle, and even mathematically sophisticated folks can stumble on them. This problem is an especially subtle one, but it’s wonderfully instructive for people who take the time to work their way through it.” I agree, of course!

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Since Benno "Head-Up-My-Ass" Bonke said:

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You said, “Yes. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.”

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then Marilyn "Not-As-Smart-As-I'm-Portrayed" Vos Savant should have replied something along the lines of "Hey, you Dutch moron, don't be putting your loony fractions into my mouth! There's this megalomaniacal putz in Illinois who posts on a language board who will jump all over your screwed up math!"

But she didn't. This, of course, provides one more bit of weight to the side who argue that she's not all that brilliant regardless of what her publicist (and TrossL) says.

And, now that I'm ranting on the subject, "Marilyn Vos Savant"?? Does this strike anyone else as being just a bit too much of a coincidence for a person writing a column of this sort?

I agree, CJ. You must be able to articulate well or what the hell good is it to be smart? I have known brilliant professors from ivy league schools who muddle through explanations so badly that the students are more confused after leaving class. Now, what good is that?

IQ tests are useful as general measures, but to say the "highest score ever" is ludicrous.


As for her name, yes, it is a bit of a coincidence. Perhaps she is only a figment of our imagination! [Where did that phrase come from anyway?]

By coincidence I just read a book called "Conned again Watson" (I can't remember the author at the moment) which is mathematics cunningly disguised as a series of Sherlockian tales. The goat/car problem is one of the ones in it (in the slightly different form of determining which of three graves contains a body). It's very well explained and if anyone is interested next week I'll post the explanation and some more of the similar intuitively misleading conundrums from the book.

Non curo ! Si metrum no habet, non est poema.

Read all about my travels around the world here.
Read even more of my travel writing and poems on my weblog.

Please do, Bob! If you have the author then, so much the better!

How did I end up as the Marilyn Vos SmartyPants fanclub president? If I got paid to like her, I would, other than that, I am totally neutral on the subject.

OK, the book is too long to quote so I'll paraphrase in terms of the car/goat and I'll make the contestant CJ and the quizmaster RE.
For the sake of argument let's put the car behind door 1 and goats behind doors 2 and 3.

CJ chooses a door.
If he chooses door 1 then RE can choose either of the others before asking CJ if he'd like to switch.
Here if CJ switches he gets a goat (boo). If CJ doesn't switch he gets a car (yeah !)

What if he chose door 2 ? Now RE HAS to choose door 3. Now if CJ switches he wins a car (Go CJ !) but if he sticks he gets a goat (shame).

OK. So much for 1 and 2. What about 3 ? No RE has to choose 2 and if CJ switches he gets a car (do it CJ !) but if he sticks it's the goat (poor CJ).

Now at the start CJ had a free choice of doors. So by the time we reach the end game if he switches there are two ways he can get the car by switching and only one way he can get the goat.

If you want empirical proof get three match boxes and a marble and a small child and play it as a game counting up the wins and losses.

The book - which is pretty good at explaining all this kind of stuff is Conned Again Watson by Colin Bruce ISBN 0-7382-0589-3.

On the other hand knowing CJ he'd probably rather have the goat anyway !

Non curo ! Si metrum no habet, non est poema.

Read all about my travels around the world here.
Read even more of my travel writing and poems on my weblog.

Interesting way of explaining it! I think I get it, yet I remain a bit confused. Logically, it seems to me that there is always a 1 in 3 chance.

Ver-r-r-ry interesting! I see the logic and humbly admit to not getting it without BH's step-by-step explanation.

And TrossL, I believe it was in some past outside-this-board communication that you expressed your undying admiration for Marilyn Von SmartMeister. I still think she's overrated.


And lastly, on an only semi-related note, I received an interesting job offer just this past week, I kid you not, TO MILK GOATS!! It seems that goat milk is considerably denser/more nutritious/more profitable/whatever (I didn't listen that closely to the whole pitch) than cow's milk on a pound-for-pound or gallon-for-gallon basis but there seems to be a shortage of people willing to do the actual milking.

The fact that this is an odd way to pick up some spare change intrigues me (not to mention how great that would look on my resume!) but, in the end, I decided not to take that career path.

Oh, CJ! I can just see you sitting on a very tiny stool milking goats! While in Olean, NY a couple weeks ago, I did pass Cutco Cutlery and couldn't help but think of you!