Statistics 101

There is an easy way to work it out - although the problem is difficult enough that it's not going to be immediately obvious.There are three possibilities.You choose the right door (p = 1/3) and Monty choses a losing door (p = 1) The probability of that is 1/3 . 1 = 1/3You choose a wrong door (p = 2/3) and Monty chooses the other losing door (p = 0.5). The probability of that is 2/3 . 1/2 = 1/3You choose the wrong door and Monty chooses the winning door which also has probability 1/3.When you see Monty open a losing door the third possibility is eliminates so you divide the other two probabilities by the probability of the third option NOT occurring (1 - 1/3 = 2/3). And (1/3)/(2/3) = 1/2Or, even easie,r note that you are reduced to two equiprobable options and it follows from that that the probability is 0.5.Monty's behaviour is absolutely crucial to this problem. Dealing with different versions might be a good exercise for your class.

Yeah, that's kind of strange. I seriously doubt God would hook you up in that way. I've wondered why some people seem predisposed towards some things and not others. I'm sure, as with most things, there are no black and white answers. In lieu of that I would offer this caveat about disease and sin. Its a convenient scapegoat to say that our sin is really because we are diseased. That way we aren't culpable for our bad choices. However, diseases and disorders actually do exist. I only question how much we should rely on them to explain our behaviors. At the same time, we have a group who says that everything bad that happens is because we're just a bunch of sinners. What ends up happening is they beat themselves up over things that are legitimately difficult for them to overcome.Maybe the best way to deal with it is somewhere in the middle.What are your personal thoughts about gambling addictions, or addictions in general?I have an addiction to nicotene. Always have. Its still hard for me to stay away, especially in social settings where its prevalent. Some people don't like it and have no problem with it. At the same time, I can count on my hand how many times I've gambled. Its not a driving force in my life by any stretch of the imagination. But for you, obviously that isn't the case.

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"A man can no more diminish God's glory by refusing to worship Him than a lunatic can put out the sun by scribbling the word, 'darkness' on the walls of his cell." -C.S. Lewis

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I don't see how reading and comparing numbers is a function of probability. That's just a function of using your eyes.

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It's information relevant to the probability. Given that the numbers drawn match those on your ticket you know that you've won. It's that simple.

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Look, if I'm wrong, then there's somebody out there making a killing in the lottery - or at a casino, or somewhere - by having their friend read the numbers/cards to them instead of just looking at them directly.

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Only if your friend is precognitive. Casinos would go out of business if they let punters bet knowing the outcome. That's why they don't allow it. Is your friend precognitive ? If not how does he know the outcome at a time when you can still place a bet or buy a ticket ?

Too simple, in fact, to be relevant to probability. It's just nonsense dressed up in probabilistic language. "Given that you are you, what are the odds that you are you"? and the like. I don't see where that's stipulated in Mod's example. He's telling me that your odds of winning go up as your friend reads the numbers to you compared to if you look at the numbers all at once.So, let's see it happen. Somebody go win the lottery by buying a ticket and then, rather than watching the results on the news, having their friend read them the numbers the next day.I agree it only works if your friend reads you the numbers as you buy the ticket, but your issue is with Mod in that regard, not with me.

Precisely...well, almost.Crash, Modulous was simply pointing out that the odds that the winner of the lottery actually has the winning lottery ticket in his hands is very nearly one (he discussed delusion and computer or reporting error as factors that would make the probability not exactly one).However, the odds that the winner won in the first place are 1 in 146 million. That does not change after the fact. Modulous was not disagreeing with you on this point at all.He was simply calculating the probabilities for two different scenarios.One - the odds of someone having won the lottery = 1 in 146 millionTwo - the odds that the winner has actually won = very nearly oneI'm not sure why he brought it up or how it pertains to nator's OP, but its irrelevance does not negate the fact that he is right.{ABE: This article might help shed some light on what Mod is talking about.In 2005 the NY Daily News published a "Scratch n Match" number that was incorrect. Thouands of people scratched off and got the erroneous number. Their odds of actually having the winning ticket in their hands based on the information they had was very nearly one. The odds of their having won were 1 in x (x being a number I do not know because I do not know the details of the drawing).After the error was discovered the odds of those people actually having the winning ticket in their hands was 0 even though the odds of their having won was still 1 in x.Hope that helps}Edited by Jaderis, : No reason given.

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Too simple, in fact, to be relevant to probability

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It obviously is relevant to the probability. Any informaton that lets you make a better guess at the outcome is relevant to probability. And what could be more relevant than actually knowing the outcome ?

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I don't see where that's stipulated in Mod's example.

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Well that's the problem isn't it ? You don't understand what Modulous is saying.Look at Message 16 again. Do you see ? The Powerball result is in. The numbers have been drawn from the machine. The numbers that were actually drawn match those on the ticket. The probability that Modulous has won GIVEN THAT INFORMATION is very different from the probability of winning without it. That's the point. Message 21 is also predicated on knowing what the winning number is. Message 25
Emphasis mine. THe key fact is knowiing the outcome, yet again. Multiple confirmation that the ticket has won. Do you see ? How can you have any confirmation unless the outcome ff the draw is known ?It's absolutely obvious that Modulous is talking about reassessing the probability based on extra information - in this case knowledge of the winning number. Edited by PaulK, : No reason given.

I have to agree with Jaderis and Nator that Modulous critique, though I would agree, is adding a superfluous element. Obviously Nator is referring to the odds before winning.That said, its unquestionable that the House almost always win. In Vegas an individual may get lucky at blackjack or at slots, but when compared to how many people in the whole population of the casino is losing, its unquestionable that the House always wins. I mean, they'd go out of business if it were any other way. This is so obvious that my mentioning of it practically a redundancy.Bars have gotten in to the game too with video poker. Its big business because even though one or two people get a decent payout, the overall trend is that you lose far more than you win. When you compound that statistical fact with every one that plays, it makes the gambling industry quite lucrative.

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"A man can no more diminish God's glory by refusing to worship Him than a lunatic can put out the sun by scribbling the word, 'darkness' on the walls of his cell." -C.S. Lewis

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So, what do YOU think are the consequences of people not understanding probability?

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A message board thread that redlines.

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Actually, if their god makes better pancakes, I'm totally switching sides. -- Charley the Australopithecine

Luck exists?Thatys breaking news, really, thats got to be sillier than both mine and nators positions.BTW, siding with her, won't win her to God.

Your problem, and everyone else in this thread (maybe) is that your confusing the odds of winning the lotto, with the possibilities, or combinations.When they give odds for winning, it is really nothing more than the possible combinations, thats it. They aren't, IMO odds for you personally.To discount the math involved in figuring out what numbers a person would pick, verses numbers drawn, is a discredit, to the term odds, in a lotto.i.e. some people have no chance at all of winning the lotto, and they never will.That is why I say the person who wins on the first try, has an odd of 1-1. How to figure that out, is beyond me. [qs]vwe can tell you, on average, how long it will be before somebody wins./qsNo you can't. Not accurately. Well thats part of my point, you would then not only factor in the chances of a number coming out, you would then have to factor in the possibility of the number picked by the machine, combined, with the chance of a particular number coming out. IMO there is no way to accurately do that.But if someone wins on the first try, then it was obvious, that their chance were 1-1. because they won. To deny that, is to deny raw data.

Now that is about as silly as anything anyone has ever posted.Why would ANYONE ever want to "win someone to God?"As for the rest, sure luck exists. It's not controllable or repeatable or subject to testing either.

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Aslan is not a Tame Lion

Yes, I understand.My rebuttal is that the question of whether or not you have the winning ticket given that you have the winning ticket is not a probabilistic function; it's linguistic legerdemain.And it's a pretty considerable waste of time. Why are we even still talking about this?

How many times to I have to refute this? Would it be possible for you address maybe just one of myriad posts I've spent rebutting this obviously fallacious reasoning?The odds of heads coming up on a fair toss of a fair coin is 1/2. That's always true, by definition, regardless of whether or not you pick the coin up and put it in your pocket and never flip it, ever. The actual outcome has absolutely nothing to do with the odds, because the actual outcome doesn't change the sample space. Knowledge of the winning numbers doesn't change the sample space, and it doesn't increase the number of outcomes that are desirable, so no, the probability doesn't change.

Oh, for god's sake. There's enough nonsense in this thread so far without you adding to it.Could you go back and address, perhaps, one of the copious posts I've created so far on this very topic? That's exactly what they are, because lottery tickets are indistinguishable. Hell, I mean, when you think about it - you don't win the lottery, your ticket does.Because there are 146 million combinations of numbers, and every ticket represents one such combination, and the winning combination is selected at random, each ticket buys you a one in 146 million chance of winning.Another way to say that is that if you played the lottery over and over again, buying one ticket each time, on average you would win once out of roughly every 146 million times you played. No, of course you can - not only that, you can tell exactly how accurate your determination will be. Statistics and probability give you a way not only to estimate, but to estimate the accuracy of your estimations.Think of a coin toss. (Fair coin, fair flip.) Not only do you know how often heads will come up - on average - you can make a determination of how many times you have to flip until you can be 95% certain (for instance) that the flipper has seen a heads result.This is the sort of estimation that statistics allows you to do. I suggest you read up on it sometime. Probability isn't a way to see the future. It's a way to make determinations about events based on the relationship between desired outcomes and all possible outcomes. Only because you're apparently completely ignorant of statistics. Indeed, because we know the scope of what numbers a valid lottery generation generates, it's trivial to determine the sample space.The number of desired outcomes compared to the number of outcomes in the sample space is the probability of a desired outcome occurring for that trial. It's the simplest math in the world which I why I'm perplexed that so many intelligent people are getting it so completely wrong. This is just a phenomenally ignorant statement. You have no idea how to figure probabilities, do you? In this case, it's really simple. How many possible numbers can be generated by one lotto drawing? (Remember that you have two sets of balls, each with the numbers 01 through 42; the first 5 numbers are drawn from the first set and the Powerball is drawn from the second. A winning ticket matches the first 5 numbers in any order and the Powerball exactly.)Once you have the sample space, you compare that to how many numbers appear on each ticket - 1 - and you have the likelihood of winning the lottery with one ticket. (Better to take your dollar and spend it on some gum.)

Flood< explained.....