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Author Topic:   Statistics 101
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 16 of 199 (386543)
02-22-2007 10:53 AM
Reply to: Message 13 by crashfrog
02-22-2007 10:21 AM


After the fact, the odds of you having won are 1 (almost).
The odds don't change after you win.
What odds don't change? Rhetorical question, with the intent of showing that I am talking about odds for a different thing.
In the case of the Powerball, that's 1 in 146 million. Before, after, it doesn't matter. The actual outcome doesn't change the probabilities of any of the outcomes.
Correct. There appears to be a communication problem happening. I'll word it in an alternative manner in the hopes that any problem with communication that came from me can be resolved.
The scenario: Every number I need to win the Powerball has come out of the machine. I have a single ticket that has the corresponding numbers printed on it. I have just gone to Lottery agency and they have confirmed that I have won and right now I have handed some contracts back to them with whatever legal stuff one has to sign to begin collecting a jackpot.
The odds of me winning the Powerball: 1 in 146 million.
The odds that I have just won the Powerball: almost 1.

This message is a reply to:
 Message 13 by crashfrog, posted 02-22-2007 10:21 AM crashfrog has replied

Replies to this message:
 Message 17 by jar, posted 02-22-2007 11:21 AM Modulous has not replied
 Message 18 by crashfrog, posted 02-22-2007 11:26 AM Modulous has replied

  
jar
Member (Idle past 394 days)
Posts: 34026
From: Texas!!
Joined: 04-20-2004


Message 17 of 199 (386546)
02-22-2007 11:21 AM
Reply to: Message 16 by Modulous
02-22-2007 10:53 AM


The IRS will most certainly agree with you.

Aslan is not a Tame Lion

This message is a reply to:
 Message 16 by Modulous, posted 02-22-2007 10:53 AM Modulous has not replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 18 of 199 (386547)
02-22-2007 11:26 AM
Reply to: Message 16 by Modulous
02-22-2007 10:53 AM


Rhetorical question, with the intent of showing that I am talking about odds for a different thing.
What different thing?
The odds that I have just won the Powerball: almost 1.
I still don't understand. The odds that you've just won the Powerball are the odds that you hold the winning ticket; the odds that that's the case are still one out of all the possible combinations of numbers; that's one in 146 million (or so.)
I mean, think about it, Mod. What happened to all the people who didn't win? They didn't fall off the Earth. They still hold losing tickets. They're still in the sample space.
We don't clear the sample space just because an outcome occurred. The fact that an outcome happened doesn't change the probabilities of the outcomes.
You're showing the kind of thinking that leads people to misunderstand things like the Monty Hall Problem. The odds don't change just because an outcome happened.

This message is a reply to:
 Message 16 by Modulous, posted 02-22-2007 10:53 AM Modulous has replied

Replies to this message:
 Message 19 by PaulK, posted 02-22-2007 11:44 AM crashfrog has replied
 Message 21 by Modulous, posted 02-22-2007 11:54 AM crashfrog has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 19 of 199 (386550)
02-22-2007 11:44 AM
Reply to: Message 18 by crashfrog
02-22-2007 11:26 AM


I think that Modulus means that the probability that you have won given that you have the winning ticket is 1 (i.e. it is a conditional probability and not a very interestign one). The prior probability - the odds against winning without taking the draw into consideration - remain unchanged.

This message is a reply to:
 Message 18 by crashfrog, posted 02-22-2007 11:26 AM crashfrog has replied

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 Message 20 by crashfrog, posted 02-22-2007 11:52 AM PaulK has not replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 20 of 199 (386553)
02-22-2007 11:52 AM
Reply to: Message 19 by PaulK
02-22-2007 11:44 AM


I think that Modulus means that the probability that you have won given that you have the winning ticket is 1 (i.e. it is a conditional probability and not a very interestign one).
I don't understand how that's a question of probability, then. It's like saying "the probability that Modulus's screen name is "Modulus", given that it is "Modulus", is 1." It's kind of a nonsense question.
I think posing nonsense questions that aren't applicable to probabilistic thinking obfuscates the issue. Mod only has the winning ticket if it's the winning ticket; and the odds of that being the case (assuming he's not a cheater) is only one in 146 million.

This message is a reply to:
 Message 19 by PaulK, posted 02-22-2007 11:44 AM PaulK has not replied

Replies to this message:
 Message 22 by Modulous, posted 02-22-2007 12:06 PM crashfrog has not replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 21 of 199 (386555)
02-22-2007 11:54 AM
Reply to: Message 18 by crashfrog
02-22-2007 11:26 AM


I still don't understand. The odds that you've just won the Powerball are the odds that you hold the winning ticket; the odds that that's the case are still one out of all the possible combinations of numbers; that's one in 146 million (or so.)
Crash, you think I am misunderstanding something here. Of all things I can talk confidently on, it is statistics. I have spent long hours explaining the Monty Hall problem. I have taken many classes on statistics and play poker (and understand how to calculate things like the implied pot odds and which action will produce the most positive expectation).
If I hold a ticket in my hand that has the winning number on it as confirmed by me and my partner. I go to the lottery office and they confirm it is the winning number for the correct date. They run double checks through their authentication systems and it agrees that it is a winning ticket.
What are the odds that the ticket I have is a winning ticket?
It is not less than 1 in 100 million. It is almost, but not quite, 1.
If you think at this point the chances that the ticket I have is a winning ticket is in the order of 1 in 100 million, how does anyboy know if they have won the lottery or not?
The chances that it was to be me on that date the won lottery are 1 in 100 million. The chances that it was me that got the winning ticket are 1. I have it right here in my hand. Its a winning ticket.
The chances that your internet handle here at evcforum is 'crashfrog' is very nearly 1. Twenty years ago if you were a betting man, you might consider what the odds are of meeting a person whose alias is crashfrog and debating the the way odds work on an 'internet forum' with that person are. You'll probably have worked out the odds are astronomical. The odds were astronimical then, but I don't think there is any doubt what the odds are that we are having this debate at this time. Damn near 1.
x happened.
What are the odds that x happened?
This is a different question than:
x happened.
What were odds that x would happen?

This message is a reply to:
 Message 18 by crashfrog, posted 02-22-2007 11:26 AM crashfrog has replied

Replies to this message:
 Message 23 by crashfrog, posted 02-22-2007 12:17 PM Modulous has replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 22 of 199 (386557)
02-22-2007 12:06 PM
Reply to: Message 20 by crashfrog
02-22-2007 11:52 AM


Heh
It's like saying "the probability that Modulus's screen name is "Modulus", given that it is "Modulus", is 1."
I hadn't read that when I posted my earlier post. Isn't there are a thread around here dedicated to synchronicity? Incidentally the chances that my screen name is "Modulus" is close to 0. Unless I've gone completely bananas (a possibility) there is a 'o' in there.
I think posing nonsense questions that aren't applicable to probabilistic thinking obfuscates the issue.
It does't obfuscate the issue at all. I was responding to jar who quoted nator when she said:
The odds of winning the lotto can be a million to one, but if I win it on my first try, then those weren't my odds were they?
I said:
Mod writes:
Yes they were.
Her odds of winning that lotto were a million to one when she picked that ticket up and up until the draw they were a million to one.
Nator was saying that her odds weren't a million to one. I was saying they were regardless of what we know happened later. I am of course assuming that she wasn't trying to defend a purely deterministic philosophy, but she might have been.
Mod writes:
After the fact, the odds of you having won are 1 (almost).
Which is also true. Not obfuscative at all. Nator was discussing how the odds change after the fact. It's an easy topic to get confused about, so I added my thoughts on the topic. The only change in odds is between 'the odds of winning' and 'the odds of having won'. The two concepts are easily confused and lead some to believe that the odds of winning for them changed or some such gobbledygook (other than in arguments about determinism of course).
Moreso when we start looking at statements like 'If I won the lottery I'd never play again because the chances of me winning twice are against me'. As if having won once, the odds of them winning when they pick up another ticket are suddenly worse.

This message is a reply to:
 Message 20 by crashfrog, posted 02-22-2007 11:52 AM crashfrog has not replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 23 of 199 (386560)
02-22-2007 12:17 PM
Reply to: Message 21 by Modulous
02-22-2007 11:54 AM


Of all things I can talk confidently on, it is statistics.
Then I have no explanation for why you're so adamantly, resolutely wrong. You are, though. (Please don't take my word for it, of course, but read on as I try to explain how.)
What are the odds that the ticket I have is a winning ticket?
It's the number of winning tickets - 1 - over the number of all possible tickets (that is, the number of possible combinations of numbers. It's not possible to buy a lottery ticket that isn't in the space of outcomes generated by the lotto drawing.)
So, it's one in 146 million, like I said. The fact that it's been confirmed by the lotto people as having the winning numbers on it doesn't change the probability that that ticket won the lottery. That's still 1 in 146 million.
The outcome doesn't change the odds. The simple fact that you won the lottery doesn't change the fact that it was very unlikely that you would have won. The probability of the outcome doesn't become 1/1 just because that was the outcome that occurred.
If you think at this point the chances that the ticket I have is a winning ticket is in the order of 1 in 100 million, how does anyboy know if they have won the lottery or not?
I'm not sure I understand the question. How do they know if they've won? They look at the ticket, the read the numbers on it, and then they compare those numbers to the numbers generated in the lotto drawing. If they're the same, they won.
Everybody knows how to check if you've won the lottery.
x happened.
What are the odds that x happened?
This is a different question than:
x happened.
What were odds that x would happen?
They're exactly the same question, only, in the first question, you've used a different construction to indicate the subjunctive mood. What are the odds that you won the lottery? One in 146 million, just like for everybody else. Before, after, during - it doesn't matter; the odds of the outcomes don't change just because one of them happened.

This message is a reply to:
 Message 21 by Modulous, posted 02-22-2007 11:54 AM Modulous has replied

Replies to this message:
 Message 25 by Modulous, posted 02-22-2007 12:39 PM crashfrog has replied
 Message 63 by NosyNed, posted 02-22-2007 11:52 PM crashfrog has replied

  
nator
Member (Idle past 2170 days)
Posts: 12961
From: Ann Arbor
Joined: 12-09-2001


Message 24 of 199 (386564)
02-22-2007 12:24 PM
Reply to: Message 15 by Chiroptera
02-22-2007 10:29 AM


Excellent, Chiro, I was hoping someone expert would show up and take things to another level.
So, what do YOU think are the consequences of people not understanding probability?

This message is a reply to:
 Message 15 by Chiroptera, posted 02-22-2007 10:29 AM Chiroptera has replied

Replies to this message:
 Message 53 by Chiroptera, posted 02-22-2007 8:26 PM nator has not replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 25 of 199 (386569)
02-22-2007 12:39 PM
Reply to: Message 23 by crashfrog
02-22-2007 12:17 PM


Then I have no explanation for why you're so adamantly, resolutely wrong.
I will 'read you out' with an open mind. However you have basically agreed with what I am saying in every post, notably in Message 20 where you even use the same example I do!
It's the number of winning tickets - 1 - over the number of all possible tickets (that is, the number of possible combinations of numbers. It's not possible to buy a lottery ticket that isn't in the space of outcomes generated by the lotto drawing.)
This is the perfect way to calculate the odds whether or not a ticket is a winning one without the ability to know what the numbers printed on it are.
I'm not sure I understand the question. How do they know if they've won? They look at the ticket, the read the numbers on it, and then they compare those numbers to the numbers generated in the lotto drawing. If they're the same, they won.
And after you have looked at the ticket, read the numbers on it and compared them to the lotto draw? What are the odds that it is a winning ticket?
Let us suppose that the chances of you being delusional are 1 in a billion. That means the odds that the ticket in front of you is a winning one is 999,999,999 to 1,000,000,000.
That is the situation I described when I asked -
quote:
What are the odds that the ticket I have is a winning ticket?
The answer, as I stated correctly, is nearly 1. Of course, if I later learn that I am delusional then the chances my ticket is a winning one changes again. It could be that several people all made an error which was coincident with a computer error, but that is a low probability. Thus: not quite 1, but nearly 1.
Are you sure that I am resolutely and adamantly wrong about the odds of a multiply confirmed winning-ticket being a winning ticket?
They're exactly the same question, only, in the first question, you've used a different construction to indicate the subjunctive mood.
They are not the same question crashfrog. They are quite different.
I flip a coin. You can see it is heads. What is the probability it is heads? It is not 50%, otherwise we'd never resolve one way or another what it is. It is very nearly certain that it is heads. Only an error on your part (unlikely given the simplicity of the task) or delusion (unlikely) or some other highly unlikely occurrance happened to cause you to think that the coin is heads when in fact it was tails.
The odds that it is heads. Very nearly one. What are the odds that x happened where x is 'the coin landed heads up'? Very nearly one.
What are the odds that you won the lottery?
Even when you can see the winning numbers in front of you? When your partner has confirmed it, the lottery guys have confirmed it? The lottery machine has confirmed it? The odds are still 146million to 1? What the hell was the point in getting people to check?

Here is my best example yet: 49 balls. 6 needed to win. You don't know what is on your lottery ticket, but somebody tells you if a number comes up. The odds of winning? 1 in 13,983,816
The first number that comes up is 1
It is confirmed. You have a 1.
What are the chances you will win now?
You need 5 balls of 5. There are 48 balls left. The answer is 1 in 1,712,304
A 2 is drawn. The draw is 1,2
You have 1,2
Now you need 4 balls of 4. There are 47 balls left. The odds of you winning now are? 1 in 178,365
3 comes up next. The draw is 1,2,3
You have 1,2,3
You need 3 of 3 with 46 to go. The odds? 1 in 15,180
You get the next one too, it was a 4. You need 2 of 2 with 45 left: 1 in 990
And you get the penulitmate one: 5. You need 1 ball out of 44.
Please don't tell me you think the odds of you winning the lotter at this stage are 1 in 146million!
Edited by Modulous, : last little example.

This message is a reply to:
 Message 23 by crashfrog, posted 02-22-2007 12:17 PM crashfrog has replied

Replies to this message:
 Message 26 by crashfrog, posted 02-22-2007 1:18 PM Modulous has replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 26 of 199 (386576)
02-22-2007 1:18 PM
Reply to: Message 25 by Modulous
02-22-2007 12:39 PM


And after you have looked at the ticket, read the numbers on it and compared them to the lotto draw? What are the odds that it is a winning ticket?
1 in 146 million, the same as it was before you knew what the winning numbers are.
It is the winning ticket, obviously. And the odds that it is are 1 in 146 million.
Let us suppose that the chances of you being delusional are 1 in a billion. That means the odds that the ticket in front of you is a winning one is 999,999,999 to 1,000,000,000.
This doesn't make any sense, I guess. What does being delusional have to do with it?
They are not the same question crashfrog.
I do know how to read statements in English, Mod. They're the same question, but the subjunctive mood was indicated in two different ways.
I flip a coin. You can see it is heads. What is the probability it is heads? It is not 50%, otherwise we'd never resolve one way or another what it is.
You're still not making sense. The odds that you are looking at heads is 50%, even though the coin landed heads-up.
The outcome doesn't change the probability. Only one outcome can happen, which I think we agree on. But that's already conceptually part of the initial calculation of the odds. So recognizing that only one outcome can happen doesn't change the odds, and it doesn't change the odds when the outcome - only one outcome out of many - happens.
The fact that an outcome happened doesn't change the odds of it happening, or having happened. Odds are the same in the past as well as the future. Odds are not time-dependant. The odds of a coin toss don't change simply because the coin toss happens in the future, or in the past. Just like it doesn't matter if it happens in Nevada or on the moon.
It is very nearly certain that it is heads.
As far as I'm concerned we can be completely certain that the outcome of the coin toss was heads; that doesn't change the fact that the odds of it being heads are only 50%.
Are you, maybe, confusing confidence intervals and probability? They're related, obviously, but I don't think they should be conflated.
Please don't tell me you think the odds of you winning the lotter at this stage are 1 in 146million!
You're committing the Monty Hall fallacy, though.
Of course the odds that you've won the lottery are 1 in 146 million, because you still have to match all 6 numbers. The outcome doesn't change the odds. Imagine that, instead of drawing the numbers one at a time, they generated the numbers all at once. Would you really say that the odds of winning those two different lotteries were really different?
Or imagine that you forgot to TiVo the drawing, and so you only find out the numbers the next day in the newspaper, regardless of what order the numbers were generated. Does that really change your odds?
Of course not. How you find out about the numbers, obviously, has no bearing on the odds of you winning the lottery.
In the Monty Hall game, the odds don't go from 1/3 to 1/2 just because Monty opens one of the doors. That's the mistake you're making, here. In the Monty Hall game, the odds that you picked the right door the first time are the same both before and after Monty opens a door - 1/3.
Edited by crashfrog, : No reason given.

This message is a reply to:
 Message 25 by Modulous, posted 02-22-2007 12:39 PM Modulous has replied

Replies to this message:
 Message 27 by Modulous, posted 02-22-2007 1:58 PM crashfrog has replied
 Message 28 by PaulK, posted 02-22-2007 2:45 PM crashfrog has replied

  
Modulous
Member
Posts: 7801
From: Manchester, UK
Joined: 05-01-2005


Message 27 of 199 (386584)
02-22-2007 1:58 PM
Reply to: Message 26 by crashfrog
02-22-2007 1:18 PM


the nature of how odds change courtesy of Mr Hall
Of course the odds that you've won the lottery are 1 in 146 million, because you still have to match all 6 numbers.
No, you've already matched them up. Or you have already matched some of them up. The odds of you winning when you already have five numbers is much better than having to match all six.
In the Monty Hall game, the odds don't go from 1/3 to 1/2 just because Monty opens one of the doors.
No they don't. At the beginning though, the odds of it being B were 1/3. You picked A and Monty opened C. The chances of it being in B now are 2/3. If you open B, and the prize in is B, then the chances of it being B are now 1. The odds changed based on new information. From 1/3 to 2/3 to 1. Are you suggesting that the odds of the prize being in B are always 1/3?
In that case, why, in the Monty Hall situation is the best action to always switch? Ironically, you are far closer to falling into Monty's trap by asserting that chances of winning the prize remains the same constantly.
The chances that you would win the lottery is always 1 in 146 million. The chances that you, of all people, happen to be holding the winning lottery ticket is 1 in 146 million.
Given the extra knowledge that you are holding the winning lottery ticket, you know that as unlikely as you were to win, you have won. The chances that you have won are 1 (apparantly the nearly one due to factors such as you being delusional are just confusing the issue so let's just skip over that). The chances you would win are 1 in 146 million. Two different calculations, two different odds calculations.
Let's think of this in another way. Let's say the lottery has been drawn. You don't know what the numbers were that were drawn, but you do know that at least one person won. What are the chances that you won the lottery? 1 in 146 million, right?
If somebody tells you that the first number drawn was 23, which is a number you picked. What are the chances you won now? It is not 1 146million no matter how many times you think it is.
If the lottery requires you to get 1 ball out 45 what are the odds you are a winner?
If the lottery requires you to get 2 balls out of 46, but you already know what the first ball is going to be, what are the odds of you winning?
What are the odds if you didn't know what the first ball was going to be, but you learned later that the first ball picked was one of the balls you picked?
The point of the Monty Hall problem is to show that odds are not simply about counting how many possibilities there are dividing the number of opportunities (in Monty Hall you have two possibilities so you think the chances of switching are 50% as well as staying where you were).
To convert, we have a lottery with 146 million players. Only one can win.
You pick up your ticket. And you are told that 145,999,998 of the other people are definitely losers. You are given the opportunity to keep the ticket you have, or switch with the one other person left playing the lottery.
What are the chances now that you will win the lottery? Not 1 in 146million. Not 1 in 2.
The chances are 145,999,999 in 146,000,000 - nearly 1 in fact.
Do you agree?
The fact that an outcome happened doesn't change the odds of it happening, or having happened.
The fact that an outcome happened doesn't change the odds of it happening. They do change the odds of it having happened, since we know that it happened, so the odds are effectively 1 in 1. More information.
Indeed. If you are holding a losing lottery ticket. What are the chances you will win the lottery with that ticket? Not even close to 1 in 146 million, they are near 0.
Or imagine that you forgot to TiVo the drawing, and so you only find out the numbers the next day in the newspaper, regardless of what order the numbers were generated. Does that really change your odds?
It changes the odds that you are winner yes. Before reading the paper you had a 1 in 146 million chance. Now you have read it you have either a 1 in 1 chance or a 0 chance. It gets interesting when you consider that the paper you bought was damaged and the last digit was unreadable.
You have five balls, but the sixth one is unknown. What are the chances you have won at this point? Do you think...hey I've five balls but the chances of me winning are still 1 in 146 million. Or do you think, there are x amount balls it could be, one of those balls means I win. Thus the chances are 1 in x. I don't know how Powerball works, but in the UK the odds are 1 in 44 that you are a winner in this position (there are 44 balls left, 1 of which makes you a jackpot winner).
Edited by Modulous, : No reason given.
Edited by Modulous, : No reason given.
Edited by Modulous, : No reason given.

This message is a reply to:
 Message 26 by crashfrog, posted 02-22-2007 1:18 PM crashfrog has replied

Replies to this message:
 Message 29 by subbie, posted 02-22-2007 3:17 PM Modulous has replied
 Message 30 by crashfrog, posted 02-22-2007 3:24 PM Modulous has replied

  
PaulK
Member
Posts: 17822
Joined: 01-10-2003
Member Rating: 2.2


Message 28 of 199 (386587)
02-22-2007 2:45 PM
Reply to: Message 26 by crashfrog
02-22-2007 1:18 PM


Sorry, Crash
Modulous is right. It's all about conditional versus unconditional probabilities.
In the Monty Hall example it is assumed that Monty intentionally picks a losing door. Since he can do that no matter which door you chose it doesn't affect the probability. If Monty chose a door at random, and it was a losing door that WOULD affect the probability that the door you chose was a winner - it would rise to 0.5.

This message is a reply to:
 Message 26 by crashfrog, posted 02-22-2007 1:18 PM crashfrog has replied

Replies to this message:
 Message 31 by Chiroptera, posted 02-22-2007 3:27 PM PaulK has replied
 Message 33 by crashfrog, posted 02-22-2007 3:32 PM PaulK has replied

  
subbie
Member (Idle past 1255 days)
Posts: 3509
Joined: 02-26-2006


Message 29 of 199 (386596)
02-22-2007 3:17 PM
Reply to: Message 27 by Modulous
02-22-2007 1:58 PM


Re: the nature of how odds change courtesy of Mr Hall
Let's think of this in another way. Let's say the lottery has been drawn. You don't know what the numbers were that were drawn, but you do know that at least one person won. What are the chances that you won the lottery? 1 in 146 million, right?
...
Before reading the paper you had a 1 in 146 million chance. Now you have read it you have either a 1 in 1 chance or a 0 chance.
This, I think, is wrong. Perhaps I am simply reading these isolated sentences out of context and am missing your point. In that event, I apologize.
Once the lottery numbers have been drawn, the probability of winning with a ticket that you purchased before the drawing are either 0 or 1, depending on whether you matched. The fact that you do not know what the outcome is does not change the probability. It is something that has already happened. The probability for any past event is always either 0 or 1.
Consider a game of draw poker where you have the 10, Jack, Queen and King of spades. What is the probability of drawing the Ace to make a royal flush? Assuming that the deck has already been shuffled and no further mixing of the cards will take place, the probability is either 1 or zero, depending on whether or not the Ace is on the top of the deck. We treat the situation as if the probability is 1 in 47 because that's all the information that we have. But our lack of information does not make the actual sequence of cards set at the time of shuffling indeterminate, or a matter of chance. The order of the cards is what it is.
Edited by subbie, : No reason given.

Those who would sacrifice an essential liberty for a temporary security will lose both, and deserve neither. -- Benjamin Franklin
We see monsters where science shows us windmills. -- Phat

This message is a reply to:
 Message 27 by Modulous, posted 02-22-2007 1:58 PM Modulous has replied

Replies to this message:
 Message 32 by crashfrog, posted 02-22-2007 3:28 PM subbie has replied
 Message 37 by Modulous, posted 02-22-2007 4:49 PM subbie has replied

  
crashfrog
Member (Idle past 1467 days)
Posts: 19762
From: Silver Spring, MD
Joined: 03-20-2003


Message 30 of 199 (386597)
02-22-2007 3:24 PM
Reply to: Message 27 by Modulous
02-22-2007 1:58 PM


Re: the nature of how odds change courtesy of Mr Hall
No, you've already matched them up.
So you've won. The odds of that happening are 1 in 146 million.
If you're asking me "what are the odds of winning, given that you've already won", you're just wasting my time. That's not a question of probabilities; that's a question of "what does nonsense mean?" If you've artificially restricted the sample space to the one outcome that actually happened, then yes, obviously that single outcome represents the totality of the sample space.
But at that point you're not doing probabilities; you're generating nonsense and obfuscating mathematics.
You picked A and Monty opened C. The chances of it being in B now are 2/3.
Yes, I know. That's what I just told you, in fact. Regardless of which door Monty opens, the probability that you were right in your initial guess doesn't change. It was 1/3 before, it was 1/3 after.
What are the odds that you've won the lottery? 1 in 146 million, regardless of whether or not you read the numbers one after another, or checked them off all at once, or had some proxy do it for you, or any number of other methods.
You buys your ticket and you takes your chances. That chance is one in 146 million.
It's really just that simple, Mod, and I can't understand why somebody who claims to know so much about probability would disagree.
Are you suggesting that the odds of the prize being in B are always 1/3?
Um, no, Mod, no I'm not. Are you even reading my posts?
If you are holding a losing lottery ticket. What are the chances you will win the lottery with that ticket?
In subsequent lotteries? That question doesn't make sense. Tickets are good for only one lottery.
It's like asking "what are the odds of winning if you don't even play"? That's a nonsense statement, probabilistically speaking. Not playing isn't an outcome in the sample space.
It changes the odds that you are winner yes.
No, of course it doesn't. Your odds were always 1 in 146 million.
Look, Mod. Odds don't have anything to do with time. That's why, if I hand you a balanced coin, and I ask you "when I flipped it this morning, what were the odds it came up heads?" you're able to answer the question.
And when I ask you what the odds of heads will be the next time you flip it, you can answer that question, too.
Even if the very next thing you do is toss the coin into a smelter and never flip it again, you can tell me what the odds of flipping that coin would be any time that it was flipped. In the future, in the past, whenever. Odds aren't time-dependant!

This message is a reply to:
 Message 27 by Modulous, posted 02-22-2007 1:58 PM Modulous has replied

Replies to this message:
 Message 38 by Modulous, posted 02-22-2007 4:56 PM crashfrog has replied
 Message 64 by NosyNed, posted 02-22-2007 11:59 PM crashfrog has replied

  
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