Statistics 101

So then explain how the lotto ticket knows what number you are going to pick? Wrong. You do not have a 1 in 146 million chances of winning. There are only 146 million combinations, thats it.If you are to accurately figure the odds, then you must do controlled experiments, and factor in every part of the equation.Your leaving out the choices made by the purchaser. And still people win on their first try, amazing. Yea, nator brought up the coin toss thing, and to tell you the truth, I am disappointed at the ability of people like you and nator to figure out the odds, of winning a coin toss.There are two sides to a coin, that gives you two chances, thats it. That doesn't mean it's your odds.Is the coin perfectly balanced?
Have you calculated every coin tood since the creation of coins?
Wind?
The strength of the flip.
The ability of the flipper.
on and on...I work with hammers, and one of the things I can do is toss a hammer up in the air, flipping it 7 or more times, and manage to catch it on the handle. It's just a feeling I have from doing it so long. I am sure if I praticed with a coin long enough, I could increase my odds of having the coin toss ending up in my favor. Factor that in, would ya.Some people play the lotto on a whim, and some people even have dreams about numbers, and then they come out. Factor that in would ya. I never said it was the combinations available, I was talking about personal odds. If you think I don't understand combinations, then stop talking to me. There are people who have won the lotto twice, holy crap, they beat the odds, they would say. How can they do that? Not for the guy who won.

It's printed right on the front.Haven't you ever played the lottery? You can do the experiment if you want, but since we know every part of the equation, we don't have to. That was Blase Pascal's big idea, after all - that you could, just from the rules of the game, determine the entire sample space for the trial.From that you can determine the probability of any desired outcome.But, if you want to do the experiment, program a computer to generate random numbers like the lotto, pick your own lotto numbers, and see how many trials it takes before your numbers win. Do it over and over again and divide the number of successes by the total number of "drawings" and you'll have the chances of winning. Depending on how long you run the program, that ratio will zero in on 1 to 146 million. His decisions aren't relevant because one number isn't any more likely than another. All combinations of numbers that are valid are equally likely, and it's not possible to buy a ticket with anything but valid numbers.It doesn't matter how the player picks his numbers; all lotto numbers have an equal chance so the odds are always the same. It's not really that amazing. Improbable events do occur - but occurring doesn't make them any more probable. You're drawing some kind of distinction that isn't there. We're talking about the likelihood of outcomes. Practically - and remember Pascal was a notorious gambler - when it comes to games we're interested in winning.When we say "the odds", we're talking about your odds - you, the player - of winning. (Nobody really wants to lose, right?) Another way to say that is your "chances" of winning. Another way to say that is your "probability" of winning.It's all the same. These terms are synonyms. Well, to be fair, we've been stipulating a fair coin toss, which means that the coin is perfectly balanced and both outcomes are equally probable. The "fair coin toss" is a hypothetical situation designed to make probabilistic concepts more accessible.In the real world, these conditions probably aren't exactly met. As for knowing "calculated every coin toss since the creation of coins", coins don't have memories, so that information isn't relevant. It's not necessary to factor that in to talk about hypothetical coin tosses, and anyway, that wouldn't be a fair toss.If we wanted to test how effectively you could do that, we would have you do it a number of times and see what percentage of those times you were able to influence the coin toss in the way that you wanted. That would give us a measure of your effectiveness at influencing coin tosses, but that information isn't relevant to hypothetical situations stipulating a fair coin toss. Your ignorance isn't improved by ignoring you.Personal odds are what we're talking about. If you buy one ticket (and again, it doesn't matter how you pick the numbers on it), you have a 1 in 146 million chance of winning, same as everybody else who buys a ticket.Look, RR, if it's impossible to figure out the odds of this stuff, how do you think the people that run the Powerball did it? They'll tell you, right on the ticket. I got the 1 in 146 million figure from their own website: No webpage found at provided URL: http://www.powerball.com/powerball/pb_prizes.asp(I've avoided mentioning before that the Powerball has a more complicated prize structure than the all-or-nothing situation I've described here, but it doesn't change the odds of winning the jackpot.) Why wouldn't they? Don't buy into Michael Behe's line of bullshit that low probabilities are the same as impossibilities.Think of all the people that try to win the lottery, even once, and never do. It's a lot more, isn't it? By several orders of magnitude. With as many lotteries as there are around the world, and as many people that play them, we should expect a few double winners over the decades.

What are the odds of tossing a head on a coin with a head on both sides:Very nearly 1.The fact that is isn't a fair coin is a new piece of information that needs to be taken into account when calculating the odds.If I hold a confirmed lottery ticket matching the winning numbers then the odds that I HAVE won are very nearly 1. I have a new piece of information upon which to recalculate the odds.Before the draw I all I know is that there are 146 million possible outcomes and I only have one random one of those. On that basis I calculate my odds.After the draw there is only ONE possible outcome and I know that I have that on my ticket. Now I calculate my odds again.

That is only true BEFORE the draw.

No, it's not new; it's just a different situation. It doesn't change any probabilities, it's a new situation where the probabilities that apply to fair coins and fair tosses doesn't apply. Obviously for such a coin there's only one outcome in the sample space.If we're talking about coin tosses, and then you pull out a die, that's not "new information that changes the probability", that's an entirely new situation. And this whole line of reasoning has nothing to do with what we're talking about. If you hold the winning ticket, you won. Simple as that. But the odds that you won were still 1 in 146 million, same as before they announced the numbers.But, you know, thanks for being the fourth person to repeat this line of reasoning without responding to any of my copious rebuttals. Suffice to say, the probabilities don't change simply because one of the outcomes has already happened. Regardless of the outcome that actually happened, the sample space still contains 146 million different other outcomes, which means that the odds that you've won are still 1 in 146 million. The fact that it happened to you doesn't make the likelihood of the outcome any greater.But seriously, though. Was there some problem with my 20 other posts where you couldn't see I'd addressed this argument already? Things that happened in the past don't simply have a probability of 1 because they already happened. They have the same probability as they did before they happened, because odds are not time-dependent.And, I'm repeating myself. Like I said go back to any one of about 20 posts where I've already made these arguments.

Ned, seriously.It's true before and after, because probabilities aren't time-dependent. A fair coin toss with a fair coin is 50% heads regardless of whether or not the toss happens in the future or the past.How many times do I have to repeat myself?

I'm coming back to re emphasize the odds calculations:BEFORE the draw there are 146M possible outcomes.
AFTER the draw -- for that particular lottery there is exactly ONE possible outcome -- the one drawn. All the other numbers are no longer possible outcomes.

Allow me to nose in as an outside observer here. This is a reply both to Ned and crashfrog. You are both right because you two are talking about two different things. However, the thing that crashfrog is talking about is a lot more helpful to us than the thing that ned is talking about.That's all. You can go back to your regular discussion.

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How many times to I have to refute this?

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Once would do if it were false. But it isn't. Don't forgget tthat for manyu of your posts you're completely misunderstanding wwhat Modulous is talking about.

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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.

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The prior probability is always 0.5. But if you have relevant information you can reasonably use a conditional probability - to use a more interesting example the modified Monty Hall problem I discussed with Chiroptera upthread.The outcome is relevant information. While it is rather trivial, the probability that the coin came up heads given that it came up heads is 1. Not 0.5. To say otherwise is to claim that the result can be changed after it happened - and that it WILL change half the time !

I'd disagree - neither is the truly relevant probability (which is not calculable).For instance the lottery is won, more often than not. And for most lotteries the total number of people who have played them is less than the number of current players. And each of them and to enter for a first time. So it isn't surprising that there are some first-time winners. It would be surprising if there weren't.Equally everyone gets some instances of good fortune. Nobody has absolutely everything go wrong. Thus it is not surprising that any particular person can claim that they've had some good luck.To look at the probabilities of the specific items of good luck happening to one person after the fact is an error. An example of confirmation bias. If something else good happened they'd use the probability of that. The relevant probability would have to take account of all the events that MIGHT have happened that would be considered good enough to use in such an argument. And obviously that is going to be higher - probably much higher - than the prior probability of the actual events.

I agree. However either 0 or 1 is not a probability. It is two probabilities.If I flipped a coin it is either heads or tails. You can work out the probability of it being heads. Its about 1 in 2. When you work out the probability of heads you don't get 1 or 0 since that is nonsense.It is like a roulette wheel. It lands on a number while you are not looking. Your friend says, "Guess what number it just landed on". What is the probability you'll get it right?If you run this test a thousand times you'll get it right once in every 37 times (depending on the wheel), thus: the probability of you getting it right on any one event is 1 in 37.If he says it is an even number and not 0. Your probability of getting it right changes. Of course it won't. And no discussion of probability will change the number that just landed on the roulette table. You still have a set probability of getting the answer right though, which is what we are talking about.

Guys, if you want to teach Crash some conditional probability, then try to do it with some examples other than the limiting cases of P(A) and P(A/A). No wonder he thinks it's nonsense And please please remember Chiroptera's essential point early on - probability only applies over repeatable trials. Consequently, trying to imply that Mod's points imply some kind of telepathy is sheer nonsense. Funny how related this is to Randman's assertion that entanglement leads to acausal communication...

Really, the lotto tickets knows the exact number I am going to pick? This is my point, a number chosen by an individual is not random.
Unless your playing quick pick. Even with the quick pick, that person has to walk in the store at the correct time, and choose a quick pick. To me, that is part of the odds. (not combinations) Yea, but if we did calculate it, and we found out the 75% of the time, it comes out heads, wouldn't that make you wonder why? Of course it matters how I pick the number on that particular drawing.
If I pick the wrong number, I don't win.Let's say I pick a different number every time, wouldn't increase the odds, or decrease them? (again, not combinations of numbers we are talking odds). Think of it as two random lines going through space, that hope to someday meet. Thanks for caring
I am not ignorant, understanding the conbinations of numbers, is childs play. I just disagree that the possible combinations of numbers, is the final word on your own personal odds, and the data shows us that people can beat the odds.
Not only that, ever see the machine that picks the numbers? Tell me that is completely 100% random. I know it is designed to be as random as possible, but is it really? I don't know who Michael Behe is.

The lottery ticket has the number that you chose (past tense) printed on it. That's what Crash means.And from the point of view of the probabilities it DOESN'T matter which number you choose. Whatever you choose the probability of winning is the same. That's because all the possible numbers have the same probability of being drawn.Here's a little exercise for you. What's the chance of you correctly guessing the outcome of a coin flip - heads or tails, assuming a fair coin. Show your working. Can you find a strategy that has a success rate that is better or worse than 0.5 ? If you are right and we have to take your strategy into account then you should be able to do that. I say that you can't find a sensible strategy that has any other probability, because you are wrong.

As both a teacher of statistics and a UK national examiner for statistics, I can assure it's not Hmmm, perhaps you need to come to one of my lessons