Is Marilyn Vos Savant wrong on this probability question?

SW VandeCarr

I just wanted to correct any misconceptions that might arise from the above. There are not many possible matching results. We are talking about the probability of one unique sequence regardless of what it appears to be. For example, pi has just one correct sequence. There is no apparent pattern to the digit sequence, but the sequence is unique.

LCKurtz

Certainly true. You can't increase or decrease the probability of selecting the winning lottery numbers no matter how they are chosen. But one thing you might be able to control is the probability of sharing the prize given that you win it. This is more a psychological problem than a mathematical one. For example, if it is true that birthday date numbers are chosen by players more often than random chance would dictate, you can perhaps increase your probability of not sharing any pot, should you win it, by avoiding the numbers 1 .. 31 in your selection.

I don't know if it is true, but several years ago I heard about a situation where some TV program had mentioned some numbers in an episode that didn't have anything to do with a lottery. But apparently several people decided to try those numbers for luck. The numbers came up and all those people got to share a much diminished prize. True or not, it illustrates my point.

Hurkyl

The point is that while we are talking about one unique sequence, many people don't think of one unique sequence and mentally replace the specific sequence with the notion of a 'random' jumble of numbers.

Studiot

I am with Hurkyl on this one.

Chiro the way to check this is to simplify.

The argument is the same if there are only two throws and thirty six possible outcomes.

I roll the dice, without seeing them, and a friend reads them 2 minutes later.
The result therefore remains hidden for two minutes.

What you are asserting is that

before the roll of the dice
P(4,3)= P(1,1)
After the hidden roll of the dice
P(4,3) > P(1,1)


I assert that
Before the roll of the dice
during the roll of the dice
one minute after the roll of the dice
10 years after the roll of the dice

that

P(4,3) = P(1,1) = 1/36


To suggest that P(4,3) > P(1,1) would admit the idea of considering comparison this for all 36 outcomes and summing to greater than unity.

If you really want to get somplicated you can consider the difference between results (1,1) and (1,1) or (4,3) and (3,4)

go well

DIABEETUS

No, she's right, depending upon the dice thrower's behavior (believe it or not)...

Assuming that the dice thrower only accounts throws that result in one of those two sequences, then yes, the likelyhoods of either having occurred are the same.

However, assuming that the dice thrower allows for ANY result, then ANY mixed sequence could pop up, and the dice thrower would then declare THAT particular mixed sequence as the one to compare with the sequence of twenty 1's. This would obviously happen WAYYYY more often than the rolling a series of all 1's.

Fredrik

I agree that it depends on the dice thrower's behavior. The fact that she doesn't mention that, and the fact that she mentions something else as the reason ("because the roll has already occurred"), makes me inclined to describe what she's saying as wrong.

Her claim: But let’s say you tossed a die out of my view and then said that the results were one of the above. Which series is more likely to be the one you threw? Because the roll has already occurred, the answer is (b). It’s far more likely that the roll produced a mixed bunch of numbers than a series of 1’s.

She's right if one of the numbers I give her is the actual sequence, and the other is a number I just made up. In that case, 66234441536125563152 is more likely to be the sequence I rolled, and 11111111111111111111 is more likely to be the number I made up. The reason is not that "the roll has already occurred". That's a garbage explanation. The reason is that the die is a better random number generator than I am.

If I had used a random number generator that's better than the die, then it would have been more likely that 11111111111111111111 is the sequence I rolled. The crappier the random generator, the more likely it is to produce a constant sequence.

DIABEETUS

Because, as you said, she never mentioned ANYTHING about assumptions about how the dice are rolled and behavior and so forth, then technically she's wrong only on the account that the inquiry is INCONCLUSIVE.... there's no way of determining the probabilities without making one of those requirements (assumptions) first. However, on a more practical level, I think its obvious that she implied to exclude such ridiculous assumptions such as: the dice thrower only accounts for rolls that produce those two particular sequences, and that the dice roller could be lying, and stuff like that. But I also do agree that her explanation is VERY, VERY vague and over-simplistic.

Bacle

Just to state that Marylin Idiot-Savant has the bad habit of posting problems without clearly explaining the "boundary conditions". It seems too, that her IQ credentials are suspect; I myself have checked in record books, but I have found no official records of her claims. It is disingenous for Idiot-Savant to claim she gives no importance to the IQ matter, and yet repeatedly posts while claimimg to have " The world's highest IQ", and it is arguably this claim that explains why most would care to read her column.

Fredrik

Her Wikipedia page explains this. Link.

Bacle

Fredrik:
Thanks for the link. What I think is dishonest about Idiot-Savant is her claiming to attribute no importance to IQ, yet including the claim "world's highest IQ" on most of her columns on 'Parade' magazine (at least last time I checked). If she made no such claim, it is likely, I believe, that there would be fewer people asking her questions.

DaveC426913

What makes you assume she is the one making that claim?

Bacle

DaveC (sorry, my quoting function is disabled for some reason):

I don't know if she's the one that makes the claim, but I assume she

knows the claim is being made, and she must know that readership

increases as a result of that claim; people want to know what (allegedly)

amazingly-brilliant has to say, not what just Marilynn Q Anonymous has to say. So, she

either uses that claim to have a larger readership (and likely be paid more), or

allows that claim to be used in her name, and yet she claims that she assigns little

importance to IQ (let alone the fact that she does not mention the controversy behind

the truth of the claim ) . But it is precisely the fact that she (allegedly) has the world's

highest IQ that attracts readers, and she must know this. I think she should either drop

the claim of having highest IQ-- if she wants to say that she attributes no major

importance --or accept that it is this claim that attracts a good portion of her readers.

And there is too the issue that she often gives strong opinions on ethical issues. I would

just like here to be consistent in her position.

DaveC426913

I ask again. What makes you think she's making this claim at all?

How can she "drop" something that someone else is saying? She's have to make an effort to make a public announcement that 'those claims people are making about me are false'.

Bacle

DaveC: I am assuming she has some control of how she is depicted, i.e., I am assuming

she has the ability to tell the paper that she does not want to be depicted as having

the world's highest IQ (it would also be reasonable for her to try to explain away the

controversy surrounding her claim). And , if she does not have that ability, she has the

choice of not writing for Parade at all (she is married to a wealthy heart-doctor, so

I doubt she needs the money). She does ofter pass ethical judgement on

letters sent to

her, so I usually like those passing judgement , who declare others as being unethical, or

describe others' actions as being unethical, to act ethically herself.

chiro

I already said in a prior post in this thread that I agreed with Hurkyl's statement that every chance has the same probability of occuring.

When I was talking about confidence, I was talking about the "believability" of getting something like 20 1's in a row. While it is true that this has the same probability as any other sequence, the "believability" of this sequence coming from a pure random process is not as believable as getting a more "random-looking" sequence.

It was this very idea of believability that I thought that Marilyn Vos Savant was talking about in the last quote, and that is why I defended her take on it.

Again, just to clarify I agreed with Hurkyl that the probability of every possibility is the same.

Bacle

Sorry for my detour.

Ii wonder if we can formalize the argument by using maximum likelihoods given

the fixed parameters of a multinomial with probability =1/6, using "backward probability"

. instead of the forward type, i.e., Bayes vs. "Standard" .

chiro

[Double post]