alanschu

No, it's a fact, and if you don't even know that you're too ignorant to continue any discussion with. Go back and talk to your professor, may be he can explain it to you, I'm tired of trying to give you a remedial education. You're the only one here discussing the probability of something being a fact Dagon. I'd rather contact your professor anyways! Besides, you would have made this point earlier had you not been backed into a corner. I agree that you should stop discussing it though. I have cited my sources (i.e. me) and have come to the conclusion that the probability that you don't know what you're talking about in this thread is 1. Of course, you may be correct one time in like a trillion years, but obviously this means we must live to be a trillion in order to witness this event. In other news, I pack bombs with me when I go onto airplanes. This is because the statistical likelihood of TWO people carrying bombs onto the planes is much less (actually impossible I have learned). As a result, I am safer.

Fair enough. EDIT: An excellent point, btw, that the probably of the 4 consecutive winners winning is another example. But he's already distorted that a lot. After all, the odds of "some person" winning he accepts as being possible. Just not anyone specifically. I just showed this thread to a friend of mine (fellow CompSci grad) and we're having some good time out of it.

I don't see any problem with my math being shoddy. Feel free on elaborating. What I see is him obfuscating the issue and utilizing probability to determine some other issue (i.e. did past reality actually happen). Effectively he is equating probability with prediction. Which is incorrect.

I am literally baffled that you just said this. You're not one to argue for defniitions? Well I can't say I'm too surprised, because you're making up definitions as you go. To make matters worse, you've just created a catch all for yourself. If you wish to declare "since the event already happened, the probably of it occurring is 1." In other words, what you just said is that the probability of the woman in the OP winning 4 consecutive lotteries is 1. Because she has done it. This is most definitely an asinine statement. Assuming you're not actually trolling, there is zero chance you attended any course on probability and are able to come to this conclusion. The only possible way you would be at the top of your class in it, is if you were the only person in the class. You have NO clue AT ALL what you are talking about. Seriously. This is a stupid comment. It's 100% wrong, has no basis in reality. The fact that something did happen does NOT mean that the probability of it occurring was 1. There is zero scientific validity in your conclusion. The world of probability theory is VERY MUCH determined by analyzing random distributions that have already occurred. At no point will you EVER see any respected statistician claim that the probability of a prior, non-deterministic, event is 1. I just flipped a coin ten times, and got: H, T, H, H, T, H, T, H, H, H. If you believe that the probability of me obtaining this sequence of coin flips is 1 (and not 1 in 1024), then you do not understand probability theory in the slightest. What I suspect, however, is that you may believe that previously occurring events are deterministic. Since you think they have a probability of one, and the "evidence" of it is the fact that said event occurred, then something (or someone) determined it to be this way. I suspect this is likely highly influenced by your religious beliefs. But it doesn't hold up one iota to scientific analysis, and certainly not probability theory. It would be better if you simply stated that you believe this is an act of God, just because. At least you wouldn't end up painting yourself into a corner, making pitiful attempts to backpedal, misdirections that you're attempting to claim something else Seriously Dagon, lets recap your posts: First you state that this woman winning the lottery is either due to a scam or supernatural phenomenon. You also take a pot shot at atheism in the process (while demonstrating that you don't know what atheism stands for) Then you claim that if something has a low enough probability, we'll never witness it You then tell someone to use inductive reasoning (which is a poor suggestion) to "prove" that something with really small odds won't happen You then start obfuscating the issue with words like "pre-determined" as if the probability of any unique set drawn from cards is somehow different (hint: it's not. No matter how much you want to think it is) A few posts later you actually acknowledge that my assertion is true After acknowledging that my assertion is correct, you backpedal into claiming that you can't make a correct prediction about it (even though you can. And there's even a small chance you'll be right). In this same post you seem to think that in order for the probability of a unique sequence of cards to "matter" I have to make a prediction on them (this is wrong. Whatever unique sequence of cards I obtain, there was a unique, and exceptionally small, probability for me to obtain that sequence. This probability happens to be the same for any unique sequence of cards drawn, assuming the deck is fair) You then deny the logical fallacy you stated (and you most certainly did) in your very first point by (incorrectly) interpreting Nightshade's accusation as applying to your claim that something that has a low probability of happening cannot happen. You then claim to have been first in a probability class in your college (while at the same time executing an unsolicited ad hominem attack on a poster, which you later claim in this thread to never do. Sorry Dagon, but someone stating that you have a poor understanding of Math is not an ad hominem attack. You're failure to actually understand math and probabilities makes that poster's statement correct) You then go on to say (a lot) that the odds state it is impossible for her to win. You then insult everyone's understanding of Math Shortly after you simply claim that the school you attended was the one that "invented" nanotechnology (wouldn't it be easier to simply state the name of the school, rather than obscure and incorrect allusions that otherwise indicate that your school is probably fictional?) You then demonstrate that you don't understand independent events, stating that double winners winning twice again is 100 trillion (which is a paradoxical statement your current belief that since it the first two wins already occurred and hence have a probability of 1) You then start to confuse the issue by somehow equating "any unique person winning the lottery" as "some person winning the lottery" Editor's Note... I'm only on page 7... I'm going to have to skip some stuff I think Oh! It seems I completely missed you ****ting all over probability theory on page 7 when you said: "The chance of someone winning once we know is 1." which is just wrooooooooooong. The probability of the outcome of an event is unchanged by whether or not the event actually occurred. All you do here is state the FACT that someone one. Not the PROBABILITY of that person winning. No sense going on any more, but really, you have demonstrated that you do not understand probability theory in the slightest. Unless maybe it's some sort of probability theory that isn't actually based on science, but maybe creationism or something. I remember another professor of mine, Russell Greiner (Here is his CV btw), stressing that all sorts of people can fudge the numbers and do funny Math, but if the Math isn't correct it'll break down eventually. Your math is wrong Dagon. I'm going to give Probability professors everywhere the benefit of the doubt, and assume they didn't teach you the nonsense you are spitting out now. It's seeming more and more likely that Dagon attempted to Google some concepts and ended up biting off more than he could chew. The only way he attended an advanced class, while making elementary mistakes that are taught in the first courses of probability, is if he never bothered to attend the prerequisite classes.

Probability theory is definitely not just about predicting what is going to happen. A quick google of the term "Probability theory" demonstrates this. An awful lot of it is analyzing random phenomenon that has already occurred. State the axiom. With a source please. But it can be any one of a million individuals, not a specific individual. So? This is a red herring. The winning individual is within the subset of all other individuals. This winner had a probability of winning. What was it?

My most recent one.

Because this notion of "pre-determined" is misleading. Unless you're just stating that the odds of predicting a winner are very low. This does not preclude the event itself from actually happening, or refute that very unlikely events can occur. The reason why I brought up an "individual" is because the probability of "some person" winning STILL needs an INDIVIDUAL to win. Of the one person that wins that isn't you, is the likelihood of that person winning greater than yours?

Dagon, the incorrect assumption you're making is that the odds of "some person" winning is wholly independent of a "unique person" winning. In order for "some person" to win, a "unique person" must win. You have already conceded that it's not impossible for "some person" to win, but it's impossible for a "pre-determined" person to win. This "some person" is an individual. Are you claiming that this individual's chances of winning were somehow lower than a "pre-determined" person's chances of winning?

Noooooooooooooooo, it is NOT AT ALL what you were saying. This is VERY DIFFERENT than what you were saying. Had you said this, I am very skeptical that anyone here would have disagreed with you. I would have certainly pointed out their errors. If P(A) is exceptionally small, then obviously 1 - P(A) (i.e. the probability of an event not happening in a Binomial situation) is going to be very high. This does not refute that events with exceptionally rare occurrences are not impossible to occur.

By unique I mean pre-selected before he's won anything. How does that change the probability of a unique person winning at that lottery? Basically what I'm getting here is what you're actually saying is not that it's impossible for super rare events to happen, but rather, that you feel it's impossible to predict them.

Since this wasn't addressed: How does "some person" win a lottery subsequent times, without "a unique person" winning that lottery as well?

Elaborate. How am I not picking a unique individual? You are picking a unique individual, Chuck. What you have to be talking about is some person in the world who plays the lottery. Chuck does play the lottery. I figured that that was some obvious given he won the lottery. Your statement is nebulous to me. What is the point of it?

I actually figured this is probably the case, but Dagon's refutation of the point was still incorrect I do not claim to be a biologist

Chuck is a specific person. Unless you wish to elaborate on what you mean. Because for "someone in the world" to win, a specific person must have achieved this feat (it's a subset of the group).

Just getting one sperm is not what made you. Only a particular sperm did.

Elaborate. How am I not picking a unique individual?

Calax is stating that the odds of that particular sperm conceiving you is exceptionally small odds. Yet this event has (obviously) happened. I don't think we can conclude Calax likes to talk about sperm from his post.

Yes, and that's the point. And actually why I liked you picking the square root of 1 million because it saved me time. Since the odds of winning this lottery is 1/1000. You admit that it is possible for someone to win a lottery at 1/1000. Since winning a lottery is an independent event, the chances of someone winning a lottery that has already won one is also 1/1000. Since 1/1000 is an acceptable probability that you concede is possible, therefore it is possible for someone to have already won the lottery, to win it again. This is because the odds of winning a second lottery, having already won the first lottery, is still 1/1000. The odds of any individual winning 2 lotteries is, as you state, 1 in a million (1/1000 * 1/1000). However, since you definitively state that winning something with 1/1000000 odds is impossible, you then paradoxically must be concluding that the odds of someone winning a second lottery having already won 1 lottery MUST be 0. Not 1/1000. In your world, since winning two lotteries of these odds is impossible, you must believe that anyone that has already won the lottery has a 0% chance of winning another lottery. 0 != 0.001

You're right, I am. He has a probably of doing so at 1/1000. This is an event that you yourself agree is possible. Since it's possible for him to achieve this event, I'm not assuming that anything impossible has happened. My reason for doing so is that you stated definitively that it is impossible. I'm demonstrating that it is, in fact, possible. The only way winning subsequent lotteries would be impossible would be if the chances of you winning a lottery was dependent on whether or not you won a previous lottery. It is not.

We agree it's possible to win with 1 in a thousand odds. Chuck has won 1 lottery. His odds of winning another lottery is the fixed chance of 1/1000. What are the odds he wins a second lottery? Is it possible for him to win a second lottery at these odds?

Chuck has a 1/1000 chance of winning a lottery. Is this event possible?

Odds of 1 in 1 million are certainly not impossible. If you'd like, I could do the exact same example with 1/1000 odds. It'll just take me more message board posts to accomplish it.

I'm trying to spell it out as literally as possible though because it seems to be necessary. The odds are indeed astronomical, but not impossible. Especially when you break it down to 4 independent events which can possibly happen.

Since we've already established that this event can possibly happen, then it is possible for Chuck to win a 3rd lottery. Chuck has now won 3 lotteries. This is an event that we have deemed possible to happen. What is the probability that Chuck wins a lottery after having already won 3?

Let's try this: Chuck just won a lottery. This lottery has a chance of winning it of 1 in a million. What is the probability that Chuck wins this lottery again? If he buys one ticket one time, 1 in a million. Don't distract yourself with "one ticket" stuff. I have fixed the odds to control for it and simplify situation. The odds of winning this lottery is one in a million and is static. I will assume that you feel that the odds of chuck winning another lottery is possible. Chuck wins this lottery (an event that can possibly happen). As a result, he has now won two lotteries. What is the probability that Chuck wins this lottery again?