See literally the 2nd sentence of the article.
230 karma · joined August 24, 2013
Again, thanks. I apologize.
Because in Monty Hall, the effect of changing probability is produced not just via elimination but via process of elimination - which is produced only because sufficient dependencies exist for it: a) the guaranteed 1:2 ratio, b) Monty must eliminate a goat, and c) the goat he eliminates can't be behind your door. These dependencies don't exist in the children problem. Unless Monty's choice occurs under the constraint of avoiding the door we chose, nothing changes. Monty: "You door has a goat behind it" -- so what? Now both of the other doors are 50/50. No similar conflict exists in the other problem. No conflict at all exists in the other problem. Elimination occurs, but it doesn't allow you to do anything further. "No GG" is just one rule, and if one elimination rule isn't sufficient for Monty Hall probabilities to change, why here?
And elimination of what? The elimination not of a possibility, but of a probability? Does that statement even have rational meaning? I'm being dead serious - we can give it mathematical meaning quite easily, but does it even have meaning to begin with?
Yes, I apparently misread that one too. But again, I disagree on the issue of whether the form of the proposed analogue matches the original problem.
I misread A. I agree that it's 1/3 if you flip pairs until at least one is heads. I disagree that living in a world where pairs of tails don't exist and living in a world where pairs of tails do exist but are ignored are the same thing.
>Are you somehow suggesting that the probability distribution of the other options is changed by this?
Yes. I'm saying it's an unwitting double Monty Hall. The fact that he can't give you 3 cars changes the odds. Going (invisibly) from 4 possible worlds (including GG) to 3 changes the prob dist of the remaining 3, by which I mean 2. If Monty must guarantee you at least one boy, then there aren't really 3 remaining possibilities. The unguaranteed can be a boy, or it can be a girl. What is the third?
>"The two" ?? What "two"? Your "explanations" are very unclear.
The only two there are: the two children. The sex of one is independent from the sex of the other.
>You will find many things difficult if you don't learn how to slow down, take time, be precise, and explain clearly. Be more like Feynman - take time to explain things clearly and precisely.
Okay, I'll try, good buddy. Monty Hall is different because it precludes upfront the possibility of there being any ratio other than 1:2. If we were, however, to say that any door could have either a goat or a car, then Monty's elimination of some other door would not inform you on the odds of your door YOUR door. Yea or nay?
The only way for Monty to give you any information at all about whether to switch is if the rule binds him to tell you something about the odds of the unchosen doors. In the original problem, this happens, because the ratio is bound 1:2. In our revised problem, this does not happen - unless he tells you he can't remove a door because neither is a goat. But! Using this as an analogue to our children problem, we've already precluded that possibility upfront by eliminating GG, thus Monty can't provide us any information because his B-G choice is unbound by any rule.
Aha! But he can't! Do you see? He can't open a door with a car, so he can't flip a coin in the event that the car is behind a door other than yours. He is bound by the rules not to do so.
1/3 your door is good; 2/3 your door is bad. If bad, he MUST leave you with the good door to switch to. So in 2/3 of scenarios, you have a 100% likelihood of winning if you switch.
The answer to all 3 is 1/2. GG + "at least one is a boy" is not a possible world, but you are calculating the probability of the others, initially, as if it were, and then asking another question on top of it. You can't do that. BB is only 1/2 as likely as BG/GB if GG is a possible world for the question to begin with.
The two are independent variables, man. I don't know how to explain it any more clearly than that. What's tripping people up is the idea that removing GG from the possibilities doesn't affect the local probability of either particular child being girl. It does. You must reformulate. THAT's the counterintuitive part. It's just hella hard to explain, because there are too many 2's and 1/2's floating around the problem, so when you say one cancels another, people think you're not incorporating the first to begin with, so you must be one of the dolts the author is trying to learn some knowledge.
The following, you can take or leave: probability is my thing. I got Monty Hall right when I was in 6th grade. I was an AIME invitee, if you know what that is. I got 800 on the math SAT; 36 on the math ACT in freshman year. None of these things mean anything, logically speaking, I know. I say them only to encourage you (and only you, because you're putting in effort) to consider what I'm saying as fully as you're considering what the crowd is saying.
>The most obvious way to do that is to talk about the older and younger.
Exactly. The father doesn't talk about older and younger, but the table does. What it should look like, because you're correct that age is irrelevant: B (given) * [b|g] -> [Bb|Bg], or if you account for age: [B is first|B is second] * [b|g] -> [Bb|bB|Bg|gB]. But you have to pick one or the other! Either way, it works, but you have to account on both ends, not just one. He's calculating for BG as if age were relevant, but it's not.
The computer "simulation" is wrong because it is grounded in the logic that one child's sex wasn't a given all along, when in fact it was. NB: if you're throwing results out, that's a bad sign.
Yea/nay?
Or, again, you can just step back and say: X is a boy. What is the probability that Y is a boy? Why on earth would it matter what X was? Do you meet 2/3 women because you are a man?
In GB and BG, he has only one way of telling you which is the boy. In BB, he has two. Thus, four possibilities a) GB, b) BG, c) BB and he gave you the first, d) BB and he gave you the second.
Your brain will of course refuse to process the above due to your earlier remark and the sweet, sweet motherfucking irony it would mean.
Yes you have! To run the experiment, you have to treat TH and HT as different but you "pretend" not to do so by adding them into the same pile. You're pretending to know that the father tells you which child is the "known boy", but by the statement of the problem, you don't know that. Why is this an error? Because the father must follow a rule - he must give you a boy, and there are two ways for him to do that in BB but you only recognize one. If you go the "table-minus" route, which both the author and your experiment do. But you can't do that without affecting the odds! By telling you they aren't both girls, he lowers the chance that either of them might be. Yes, I'm serious.
Correct formulation of table:
a) BG; b) GB; c) BB and he gives you the first; d) BB and he gives you the second.
You misunderstand Monty Hall. I would know; I learned about it by being asked the question and getting it right, not by reading someone else's explanation (which leaves room for misinterpretation). The key to Monty Hall is none of what you stated (or rather, rhetorically asked); it's that the host must pick a door that is both a) bad and b) not yours. If your door is good, then he can leave either, but if your door is bad, then he must leave the good one. So, two possibilities: the door he left was either bad or good, BUT the rule driving his choice wasn't 50/50, so the odds of it being bad or good aren't 50/50, so neither are the odds of yours, even though there are only two left. Take a minute, think about it.
Now ask yourself which "door" (read child) the father told you was a boy. There's the gotcha. Under your/the author's formulation of the question, he doesn't remove a door in the BB universe, but he does in the BG universe. There are two BG's because the table acknowledges that he can tell you which of the two is definitely a boy, and thus he has two options for doing so BUT HE DOESN'T, HE HAS ONE BUT THERE ARE TWO BG UNIVERSES, SO IT LOOKS LIKE TWO.
In oversimplifying your table for potential idiot readers by introducing the silent variable of older vs younger child, you have introduced order into a statistics problem wherein order is irrelevant and masked the fact that what matters is which of the children you already know to be a boy. You grant this difference for the BG pairing, thus producing two options, but not for the BB pairing. There is not ONE way of knowing this for BB, as you present in the table, but two: you know the older is the boy, or you know the younger is the boy. 2/4 = 1/2. QED.
What you should have done in the first place, however (unless your aim is to produce a blog post which, apparently, can convince otherwise intelligent people that irrelevant information can magically become relevant) was simply remove the one boy from the equation and reformulate the question. What is the probability that this other child is a boy (and thus that both are boys)? 1/2. Fuck the table. Had you not used a table, this would never have happened. But it feels authoritative, right? Thank you for the psychology lesson.
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Downvotes but not refutations, because there aren't any. I'll assume it's my tone. My opinion of the competence of the average reader on this site has plummeted reading the other comments, however, so hey, fuck you guys too. :)
Why not bypass this and go straight to the device? Imagine paying for internet and not being limited to your house. Then you can expand your "work somewhere which is not your home and not your office" options beyond just Starbucks, et al. Plus the more different you are from the current business model, the better; you have a greater variety of ways to sell yourself, e.g. "This Internet Option, for the on-the-go professional who doesn't have time for wires!" or "Comcast wants you to have a modem. Lol, ok, Grandpa. Eyeroll.gif" or even "Gee Honey, you were right about This Internet Option. I never realized how much more alive - and sexy, and free - I feel using my laptop on the backyard swing!" Also you could compete on price (dramatically so!) with mobile carriers, if your network of boxes is, say, at least city-wide. Home, work, and between.
(Sorry about that. I was having fun.)