Woman wins millions in lottery 4 times!

[Humodour]

Crap, I spelt googol incorrectly. Damn you Google for bastardising the spelling of your namesake.

 

Edit: Look at it this way Wrath - events with very very very small chances of occuring happen all the time. For most of those events, they do not occur. But because so many of them happen daily, you're bound to find some that do occur. Winning the lottery 4 times in a row is one such event. Although in this case the gambler's fallacy should be kept in mind: once she's won the lottery 3 times in a row, her chance of winning it a 4th time is actually the same as anybody else's - very low, but SOMEBODY has to win it and her odds are as good as anybody's. There is no cosmic censor saying "you've already won it 3 times before, you can't win it a 4th time".

Edited July 15, 2010 by Krezack

[Wrath of Dagon]

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.

No, it was the university that invented nano-technology.

 

And yes, I know infinitesimal means the value of a variable as it approaches 0. I was using the term in the colloquial sense of very close to 0, as pointed out previously.

 

And Balthamael, your math is completely wrong, I'm too lazy to go into why. Normally the chances of winning the lottery are about 1 in 16 million, from that the chances of someone winning 4 times is about 1 in 100 trillion. Remember, she's not the only one who's playing the lottery, and all we need are the chances of someone winning 4 times in one of the lotteries in the world over a period of a few years say, not necessarily this particular person.

 

Btw, I guess there's also the possibility that the story is a hoax to start with.

[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.

No, it was the university that invented nano-technology.

 

No university 'invented' nanotechnology. Feynman described the new science of nanotech in his awesome speech "There's Plenty of Room at the Bottom" - go read it everyone! He is the father of nanotech, not any university research group. I also take issue with the notion that nanotechnology was 'invented'. Nature (as in evolution) has been practicing it for millions of years.

 

And yes, I know infinitesimal means the value of a variable as it approaches 0. I was using the term in the colloquial sense of very close to 0, as pointed out previously.

 

And Balthamael, your math is completely wrong, I'm too lazy to go into why. Normally the chances of winning the lottery are about 1 in 16 million, from that the chances of someone winning 4 times is about 1 in 100 trillion. Remember, she's not the only one who's playing the lottery, and all we need are the chances of someone winning 4 times in one of the lotteries in the world over a period of a few years say, not necessarily this particular person.

 

Btw, I guess there's also the possibility that the story is a hoax to start with.

 

You believe a person can win the lottery once, yes? A small chance, but it exists.

 

Once they've won it once, their chances of wining it again are the same as anybody else's. So they might win again. That would mean they've won 2 times. Fine, right?

 

Once they've won 2 times, their chances of winning again are still the same as anybody else's. So they COULD win 3 times. And the same way, they could win 4.

 

If you believe a person can win the lottery once, to be logically consistent you should believe they can win the lottery 4 times.

 

Of course if all you're saying is "cool, that's amazingly good luck" not "it's impossible - it must be a supernatural force", then yeah, I agree.

Edited July 15, 2010 by Krezack

[Wrath of Dagon]

Her chances of winning again are 1 in 16 million. Her chances of winning 4 times are 1 in 100 trillion. The only reason it's not surprising she won the first time is because someone has to win. It's not surprising the second time because there are thousands of lottery winners spending thousands of dollars to play lotteries, so one of them will win again every few years. After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

[Humodour]

Her chances of winning again are 1 in 16 million. Her chances of winning 4 times are 1 in 100 trillion. The only reason it's not surprising she won the first time is because someone has to win. It's not surprising the second time because there are thousands of lottery winners spending thousands of dollars to play lotteries, so one of them will win again every few years. After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

 

You don't understand probability.

 

There's a bunch of mathematicians on this forum, as well many who took maths subjects at university. Please, please, please believe us when we say that you are simply incorrect, even if you still don't understand why.

 

The notion that somebody would go around wilfully believing that events with small likelihoods of occuring are actually impossible is almost physically painful to me.

Edited July 15, 2010 by Krezack

[mkreku]

Judging from this thread, I would say that the chances of her winning the lottery four times was still higher than the probability that Wrath of Dagon actually has any university math credits to his name.

[alanschu]

After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

 

Did you just take one of the Arts Faculty's probability courses? Because this statement is wrong in any statistics course, even if it's a course from the school that allegedly invented nanotechnology (which school was this again?)

 

 

Winning a lottery is an independent event of winning future lotteries. The chances of someone winning with a lottery ticket is not affected by whether or not they have previously won a lottery ticket. I think (or at least hope) that we can all agree on this). That is, for any given lottery, the chances any one individual has of winning it is not affected in any way by that person winning a lottery previously.

 

So lets set this up:

P( A | B )

 

A is the probably of winning two more lotteries

B is the probably of winning two lotteries in the past.

 

Since A is independent of B, we know that P( A | B ) = P( A ).

 

Assuming the lotteries in A have equivalent chance to win as the past lotteries in B, then the P( A ) = P( B ).

 

Therefore, since the probability of winning two lotteries in the past is "not surprising" (Dagon's words), then the probability of winning two lotteries in the future must be "not surprising."

 

 

 

In order to spell it out a little clearer, lets use coin flips.

 

The probability of the first two coin flips being heads is 0.25 [This is pretty trivial: 0.5 * 0.5 = 0.25]

The probability of having two more coin flips that are heads having already had two coin flips that were heads is, I hope is obvious, also 0.25. Because you've already gotten two heads coin flips, the probability of you getting another 2 is irrelevant of what you got previously.

 

Though straight up, the probability of getting 4 heads in a row is 0.0625. People often assume that because the odds of getting heads 4 times in a row is low, the odds of getting that last heads when you've already gotten three is somehow lower.

 

The thing I find very interesting, is that this very concept was what many second year CompSci students struggled with when they took this course at my University (Stats 221 - In fact, Dr. Kouritzin was my Stats 221 teacher back in 2004... he actually worked for Lockheed Martin for a while too /coolfact). For most of us it was our first exposure to random variables and probability.

Edited July 15, 2010 by alanschu

[Deadly_Nightshade]

...which is clearly impossible.

 

I think you mean improbable...

Anyways, I was going to go into more detail about why you're mistaken about how unlikely it was, but Alanschu just described it in more detail and more eloquently than I would have.

[Balthamael]

Her chances of winning again are 1 in 16 million. Her chances of winning 4 times are 1 in 100 trillion. The only reason it's not surprising she won the first time is because someone has to win. It's not surprising the second time because there are thousands of lottery winners spending thousands of dollars to play lotteries, so one of them will win again every few years. After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

 

Do you think the amount of lottery tickets this lady has bought over her life is at all relevant to her chances of winning? If not, why not? If yes, how does your calculation account for that?

[Calax]

Her chances of winning again are 1 in 16 million. Her chances of winning 4 times are 1 in 100 trillion. The only reason it's not surprising she won the first time is because someone has to win. It's not surprising the second time because there are thousands of lottery winners spending thousands of dollars to play lotteries, so one of them will win again every few years. After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

They're different games. They're odds aren't dependant on one another she has 1/16 mil of winning each of them, it's not 1/16 mil then 1/32 mill because both lottery pools are thrown together.

[Wrath of Dagon]

Though straight up, the probability of getting 4 heads in a row is 0.0625. People often assume that because the odds of getting heads 4 times in a row is low, the odds of getting that last heads when you've already gotten three is somehow lower.

Exactly, and she won 4 times, so that's what you have to calculate. Also you can't confuse the odds of a particular person winning, and the odds of someone in the world winning.

 

And no, I don't think there are any mathematicians here.

 

And yes, I did take the average amount spent by people who won once into calculating the odds of one of them winning the second time. I don't think you'd take that into account for the 3rd and 4th calculation because the total odds are only divided by that number once.

[Oblarg]

After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible.

 

Did you just take one of the Arts Faculty's probability courses? Because this statement is wrong in any statistics course, even if it's a course from the school that allegedly invented nanotechnology (which school was this again?)

 

 

Winning a lottery is an independent event of winning future lotteries. The chances of someone winning with a lottery ticket is not affected by whether or not they have previously won a lottery ticket. I think (or at least hope) that we can all agree on this). That is, for any given lottery, the chances any one individual has of winning it is not affected in any way by that person winning a lottery previously.

 

So lets set this up:

P( A | B )

 

A is the probably of winning two more lotteries

B is the probably of winning two lotteries in the past.

 

Since A is independent of B, we know that P( A | B ) = P( A ).

 

Assuming the lotteries in A have equivalent chance to win as the past lotteries in B, then the P( A ) = P( B ).

 

Therefore, since the probability of winning two lotteries in the past is "not surprising" (Dagon's words), then the probability of winning two lotteries in the future must be "not surprising."

 

 

 

In order to spell it out a little clearer, lets use coin flips.

 

The probability of the first two coin flips being heads is 0.25 [This is pretty trivial: 0.5 * 0.5 = 0.25]

The probability of having two more coin flips that are heads having already had two coin flips that were heads is, I hope is obvious, also 0.25. Because you've already gotten two heads coin flips, the probability of you getting another 2 is irrelevant of what you got previously.

 

Though straight up, the probability of getting 4 heads in a row is 0.0625. People often assume that because the odds of getting heads 4 times in a row is low, the odds of getting that last heads when you've already gotten three is somehow lower.

 

The thing I find very interesting, is that this very concept was what many second year CompSci students struggled with when they took this course at my University (Stats 221 - In fact, Dr. Kouritzin was my Stats 221 teacher back in 2004... he actually worked for Lockheed Martin for a while too /coolfact). For most of us it was our first exposure to random variables and probability.

 

Admittedly, you have to be careful as you can make mistakes the other way, too.

 

Example:

 

I flip two coins. One of the coinflips resulted in heads. What is the probability that the other coinflip resulted in heads?

 

Well, obviously the two coinflips are independent, so many would jump to the conclusion that the probability is 1/2. Unfortunately, that's wrong.

 

Let's set up the problem:

 

P(H1) = probability of the first coin being heads

P(H2) = probability of the second coin being heads

 

Now, the incorrect assumption is that we're asking P(H1 and H2|H1) which obviously = P(H2) = 1/2.

 

However, upon closer inspection, it's clear that we're actually asking P(H1 and H2|H1 or H2) = P(H1 and H2 and H1 or H2)/P(H1 or H2) = P(H1 and H2)/P(H1 or H2) = .25/.75 = 1/3.

[Tigranes]

Again, I'm an idiot with maths, but just going by alanschu's simple examples:

 

Wouldn't 0.0625 be the only figure that is relevant here? That is, if the question is, "What are the chances of a person winning the lottery 4 times"? I mean, obviously, the probability will have increased every time she bought a lottery ticket, it's not 4 tickets she bought in a row that one, but still, since we're talking about the same person.

[Gromnir]

a kanadian fellow won a million or more in lotteries 5 times. the only reason Gromnir is aware is 'cause the guy were forced to sue to collect his winnings. as we recall, he won.

 

HA! Good Fun!

[Humodour]

And no, I don't think there are any mathematicians here.

 

You can pretty much count anybody who did analysis or abstract algebra at uni to be a basic mathematician mate. Aybody who has passed those subjects possess a mathemtical brain and is worth listening to when it comes to discussions of logic or statistics as they have had to formally and rigourously prove a vast number of theorems from scratch.

[alanschu]

Again, I'm an idiot with maths, but just going by alanschu's simple examples:

 

Wouldn't 0.0625 be the only figure that is relevant here?

 

Given Dagon's comments of: "After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible," he's stating that the odds of winning two more lotteries, after winning two previous ones, is somehow lower. What he is basically saying with his statement is that, if you flip 4 coins, if the first two are heads, the probability of the next two being heads are less than what they actually are. In more layman's terms, he stated that the odds of these two coin flips being heads is less than 0.25.

 

I was more addressing Dagon's incorrect statement when I started bringing in some simple conditional probabilities. It was a credibility check, as he makes mistakes that people shouldn't make after taking courses on statistics and/or probabilities. Essentially, if he was top of the class for his probability course, he either was in a very weak class, or is lying behind the anonymity of the internet.

 

As for 0.0625 being the relevant figure, the probability of someone taking a fair coin and flipping it heads 4 times is 0.0625. But I'm just (failing horrible it seems) trying to make it clear that it is not as though the prior success indicate that the next coin flip to have any other probability than 0.5. But as you flip coins as heads, the probability of achieving 4 heads in a row will improve since you've already achieved part of your goal.

 

Even though this woman has won 4 lotteries, her odds of winning a 5th are the same as some other winless lottery player winning their 1st. So if you can acknowledge that this woman has already won 4 lotteries, and feel as though winning 1 lottery is not an impossibility (which Dagon concedes), then it cannot be impossible to win a 5th. Hopefully that makes a bit more sense. It's super late and I'm off to bed now

 

 

 

Admittedly, you have to be careful as you can make mistakes the other way, too.

True, but that's not the situation Dagon painted with his statement.

 

Exactly, and she won 4 times, so that's what you have to calculate.

Exactly indeed. When you stated your example, you made probably the most common incorrect assumption that people with their first exposure to probabilities and statistics make. You should be more attentive to the issue I was actually addressing in your post. If you wish for me to not talk about aspects of probabilities not relating specifically to the likelihood of someone winning the lottery 4 times, then DO NOT MAKE ELEMENTARY MISTAKES IN OTHER STATEMENTS THAT ARE TANGENTIAL TO THE DISCUSSION THAT DEMONSTRATE YOU HAVE A POOR UNDERSTANDING OF HOW PROBABILITY WORKS.

 

Also you can't confuse the odds of a particular person winning, and the odds of someone in the world winning.

I did no such thing. The odds of someone in the world winning is going to be a function of how many winning tickets there are and how frequently tickets are purchased by everyone. Until now, no one else mentioned anything of the sort.

Edited July 15, 2010 by alanschu

[Oblarg]

True, but that's not the situation Dagon painted with his statement.

 

Not saying it was. Just a word of caution so we don't end up making that same mistake later in the thread. Also, the math nerd in me couldn't resist posting that problem.

[Deadly_Nightshade]

Sadly, I suspect that Dagon will continue to follow Dagon-Maths

[Thorton_AP]

Even though this woman has won 4 lotteries, her odds of winning a 5th are the same as some other winless lottery player winning their 1st. So if you can acknowledge that this woman has already won 4 lotteries, and feel as though winning 1 lottery is not an impossibility (which Dagon concedes), then it cannot be impossible to win a 5th.

 

Actually this makes it seem pretty clear.

[Balthamael]

Exactly, and she won 4 times, so that's what you have to calculate. Also you can't confuse the odds of a particular person winning, and the odds of someone in the world winning.

 

And no, I don't think there are any mathematicians here.

 

And yes, I did take the average amount spent by people who won once into calculating the odds of one of them winning the second time. I don't think you'd take that into account for the 3rd and 4th calculation because the total odds are only divided by that number once.

 

 

I think you are going to have to present your math before we are done here. How exactly did you arrive to the figure one in 100 trillion?

[Moose]

In your face GUIDs.

[Amentep]

Oh god, I'm having flashbacks to trying to explain the "Monty Hall problem" back on BIS...

[Pidesco]

I can't believe I only stumbled upon this thread, now.

 

This is some hilarious stuff.

[Wrath of Dagon]

Again, I'm an idiot with maths, but just going by alanschu's simple examples:

 

Wouldn't 0.0625 be the only figure that is relevant here?

 

Given Dagon's comments of: "After that, the chances of one of the double winners winning again twice is 1 in 100 trillion, which is clearly impossible," he's stating that the odds of winning two more lotteries, after winning two previous ones, is somehow lower. What he is basically saying with his statement is that, if you flip 4 coins, if the first two are heads, the probability of the next two being heads are less than what they actually are. In more layman's terms, he stated that the odds of these two coin flips being heads is less than 0.25.

No, the reason it matters that she already won twice is because at the start you have the entire pool of everyone in the world who plays the lottery who can potentially win once. But when you only count people who already won twice, you only got a handful of people who potentially could win the third time. Sure, the odds of a particular person in the pool winning are still the same as the first time, but now you only got a handful who can win at all.

 

I think you are going to have to present your math before we are done here. How exactly did you arrive to the figure one in 100 trillion?

Well, I assumed there's only a few people who've won twice, let's call it x, so the odds of one of them winning twice are approximately 16 million squared divided by x.

Edited July 15, 2010 by Wrath of Dagon

[Calax]

Dagon, no...

 

They have the same chance in each contest to win, right?

 

Then why is it impossible for them to win several times?

 

also .000000000000000001 does not = 0 in any circumstances.