Woman wins millions in lottery 4 times!

[Wrath of Dagon]

I didn't commit any logical fallacy. I said something that's extremely unlikely to happen will not happen. Some sequence of cards being drawn isn't unlikely, it has a probability of one. A particular sequence of cards that's predicted ahead of time will never happen, nothing said here changes that.

[Deadly_Nightshade]

I didn't commit any logical fallacy.

 

Yes you did. In your first post you set up a false dichotomy.

 

I said something that's extremely unlikely to happen will not happen.

 

That's incorrect. Something that is unlikely to happen is unlikely to happen.

 

A particular sequence of cards that's predicted ahead of time will never happen, nothing said here changes that.

 

Except that you're completely and utterly incorrect. It could happen, the odds are just so slight that it is extremely unlikely that it would happen. Please stop using this flawed, pointless argument that has no validity.

Edited July 14, 2010 by Deadly_Nightshade

[Wrath of Dagon]

I'm saying that something happening once in a trillion trillion years (or more closely trillion trillion trillion trillion years in this case) is functionally equivalent to never happening.

[kirottu]

I'm saying that something happening once in a trillion trillion years (or more closely trillion trillion trillion trillion years in this case) is functionally equivalent to never happening.

 

Not if you

[Thorton_AP]

I said something that's extremely unlikely to happen will not happen.

 

It's already been demonstrated in this thread that this is not true.

[Humodour]

lol @ watching Wrath's poor understanding of mathematical logic get torn to shreds. Now where's the popcorn...

[Calax]

The way I see it, there are only two possible explanations. Either this is the most elaborate scam ever, or there has to be a supernatural explanation. Take that atheists!

What about this claim? You know, the one you STARTED THE THREAD WITH!?

[Wrath of Dagon]

What about that claim?

 

 

lol @ watching Wrath's poor understanding of mathematical logic get torn to shreds. Now where's the popcorn...

I was first in my college probabilty class. It's obviously the dope that's interfering with any logical thinking on your part.

[Walsingham]

WTF?

 

She entered four competitions OF CHANCE and you want to know how she won? BY CHANCE!

[Calax]

What about that claim?

 

 

lol @ watching Wrath's poor understanding of mathematical logic get torn to shreds. Now where's the popcorn...

I was first in my college probabilty class. It's obviously the dope that's interfering with any logical thinking on your part.

You said that the only way it could happen was supernatural intervention or cheating, we're saying that it it's perfectly normal and logical to think that yes, it was probably cheating, but no, divine intervention was not needed. And that yes, there is a chance that she could have gotten it and even if there are minuscule chances, they're still chances. Saying "Little chance won't happen" is to deny the idea of chance in the first place.

[Wrath of Dagon]

What you guys seem to fail to understand is that a probability infinitesimally close to 0 is functionally equivalent to 0. Think of the rounding error in the 100th place.

 

WTF?

 

She entered four competitions OF CHANCE and you want to know how she won? BY CHANCE!

The odds say it was impossible for her to win, yet she won. Hence the conundrum. Saying "BY CHANCE" explains nothing.

Edited July 14, 2010 by Wrath of Dagon

[LadyCrimson]

I'm in agreement that no matter how ridiculous the odds, there's always the chance that it could happen, and occasionally, it actually does happen.

 

That said...I wish I had had that woman's odds-beating luck.

[alanschu]

I was first in my college probabilty class.

 

I find this exceptionally surprising.

[Wrath of Dagon]

I find it exceptionally surprising that I have to explain the obvious. This thread is like trying to give a math lecture in an insane asylum. No wonder the West is in decline.

[Deadly_Nightshade]

What you guys seem to fail to understand is that a probability infinitesimally close to 0 is functionally equivalent to 0.

 

No, you are mistaken. A probability that is, quote, "infinitesimally close to 0" might be functionally be treated as zero for piratical purposes -hence the functional-, but that, however, does not mean that the actual odds themselves change. There is still a chance that the event would occur even if the functional, likely outcome is different.

 

The odds say it was impossible for her to win, yet she won.

 

The odds say no such thing. Sorry, but, again, you're wrong. Chance can, and does, explain many things that are improbable - including this.

 

I was first in my college probabilty class.

 

I doubt that.

[LadyCrimson]

No one is arguing that it's extremely unlikely...so unlikely that 'fraud' comes immediately to mind when you hear about it (hence the investigation, obviously).

 

However, while "a probability infinitesimally close to 0 is functionally equivalent to 0" may be true in the classroom and while working on theories in the lab or whatnot, it does not, in fact, = "true 0".

Edited July 14, 2010 by LadyCrimson

[Deadly_Nightshade]

You know, if you want support your Dagon-Maths

[Hurlshort]

Hilarious double-post.

 

This thread reminds me of Shark week, for some odd reason.

[Tigranes]

You guys can't even talk about the freaking lottery without fighting.

 

I'm rubbish at maths so I don't pretend to know anything here, but is Dagon suggesting that it's impossible because the chances are so small? O_O

[Oblarg]

Going to chime in because I'm a math nerd and the math here is getting really shoddy.

 

An infinitesimal amount is, indeed, rigorously equal to zero.

 

The chance here, however, was not infinitesimal. It was simply very, very small.

 

That said, while it certainly isn't impossible for this to happen, a much better explanation is that there are lurking variables (cheating, for instance) that resulted in not-so-improbable odds of winning.

 

Edit: Upon rereading the thread, I don't think WoD quite understands the concept of infinity. An infinitesimal chance is infinitely less likely to happen than the chance of this happening. Infinity is really, really big. Infinitesimal is not a term you throw around lightly.

Edited July 14, 2010 by Oblarg

[Humodour]

lol @ watching Wrath's poor understanding of mathematical logic get torn to shreds. Now where's the popcorn...

I was first in my college probabilty class.

 

Of course you were. I'll bet that college also taught creationism as a core component of its biology degrees.

Edited July 14, 2010 by Krezack

[Deadly_Nightshade]

An infinitesimal amount is, indeed, rigorously equal to zero.

 

Wouldn't that depend on if you're using the vernacular or mathematic sense of the word?

 

...is Dagon suggesting that it's impossible because the chances are so small? O_O

 

Evidently.

[Deadly_Nightshade]

Edit: Upon rereading the thread, I don't think WoD quite understands the concept of infinity. An infinitesimal chance is infinitely less likely to happen than the chance of this happening. Infinity is really, really big. Infinitesimal is not a term you throw around lightly.

 

I think that he's thinking of the common usage, in this case simply "an extremely small number that's hard for the lay person to tell from zero", and not the stricter mathematical sense.

 

[Balthamael]

Figured that this thread might benefit from some actual math, so I took it upon myself. First watch when I pull some data out of my ass. The article mentions that the old lady won her first jackpot in 1993. So, let's assume that she has bought a ticket every week for 15 years. Probably not far from truth. That makes 780 tickets in total. Then we need to know what is the probability that a single ticket wins. Likely she has participated different kinds of lotteries and that probability will not always be the same. We, however, simplify the problem and assume that it is. The article mentions a number 1/1.8E25, which I assumed is the probability of four consecutive successes. From that, by taking the fourth root, we get

 

p = 4,8549177 E-7

number of tickets = k = 780

 

When p and k are known, we can use the binomial theorem to calculate the desired number. Without further ado:

 

Probability of at least three successes(it must be three, not four. Do you see why?) = P(X>=3) = 2.68 E-11, or 1 out of 37 billion. Make of that what you will.

 

If anyone wants to check the math, be my guest. It's 2 am and I should be sleeping, so can't guarantee that it is right. Also, if someone has some better data, by all means use it.

[Humodour]

Wrath, let me just point out to you that in mathematics (of which statistics is a subset), an infinitesimal is a different value to a very small number.

 

Indeed, in order to consider calculus the old fashion way (as Leibniz and Newton did - instead of the modern limit method) one must actually extend the number system to include such infinitesimal values - this is called the Hyperreal field.

 

My point is that infinitesimal numbers are not normal numbers. They do not have finite values as 1/google or 1/1000000000000 do. 1/google is a very very very small number. But it is a number in the Reals, and a chance of 1/google still has a very real (heh) possibility of happening. That is to say: if an event A with a probability of 1/google happened, no mathematician or statistician with any intelligence would be remotely surprised (especially if event A is repeated many times over large time intervals, as in the evolution of life for example).

 

Put simply: infinitesimals are the inverses of infinities. This is a far more elegant way of understanding why infinitesimals are not normal numbers.