They have to be. All doors were equally likely to contain the prize at the beginning (or so it is reasonable to assume), so all remaining doors are still equally likely to contain it now. The other doors are nonexistent once we know them to not have a prize.
It's simple probability. Upon knowing that the other doors are not winners, you cease to consider them (they are no longer options, unless you're acting irrationally). There are now two doors, and only one door can have a prize. Thus, the probability that yours has the door is 1/2.
It does change the odds, but not in the way you're saying. It does not change the odds of you having picked the correct ticket initially (that was still 1 in 60 million). It DOES change the odds that you currently hold the correct ticket (that is now 1 in 2, since you are now, having been given the choice to switch, making a new choice from a pool of two... unless you're dumb, and are willing to choose something you know will lose).
You (and others) are acting as if the other 59,999,998 tickets (or 98 doors) still matter. They do not matter any more, because they are not part of the pool of choices any more once you know they are not winners. This does not affect the odds of the original choice, but it does affect the odds of the new choice. You guys are repackaging the gambler's fallacy: saying that the unlikelihood of events up until now have a bearing on the likelihood of events in the future.
You are talking about a bouncing ball, that is a physical object. If it is going to bounce an infinite number of times, it will take an infinite amount of time because it will never stop, ever. Hence, infinite amount of bounces. Once you cede that the ball will stop bouncing, you have also ceded that it did not bounce an infinite amount of times.
No. It will take a finite amount of time. That does not change the fact that infinite actions can take place in that amount of time. It's important to remember that it is not merely the height of the bounce that shrinks, but also the time it takes to bounce that shrinks. Because the time for each action is approaching zero, infinite actions can happen in the finite amount of time.
The math may have involved infinity in the terms of as the number of bounces approaches infinity, but not an infinite amount of bounces.
Those are the same thing. If the number of bounces approaches infinity as t approaches 30 seconds, it means an infinite number of bounces happen in those 30 seconds. You're drawing a distinction that doesn't exist.
Of course it doesn't change the chance that you initially selected the wrong door... but that's not the point. The point is that now that you know there are only two doors which are unknown (all the others do not have a prize), you get to choose again: there are two doors, and either one may have the prize. If you pick the one you originally picked, the odds are exactly the same as if you pick the one you did not originally pick.
You are saying two things. You are saying that the chance you picked the right door is both 1/100 and 1/2.
No I'm not. Perhaps I was unclear in what I was saying. Let me try again. The probability, upon your initial choice, of picking the right door is 1/100. Now, eliminate 98 wrong doors. The probability that either of those two doors is correct is 1/2. Thus, even though the probability of you picking correctly initially was 1/100, you have made the choice. Now, keeping that door is a new choice out of a pool of 2. The original probability doesn't apply any more.
So yes, the probability that you have picked the right door from the start is 1/100 (or 1/3 in your example), however, when you decide whether to stay or switch between the two doors, it is a new choice, and the probability has to be considered independently. What you're saying sounds similar to the gambler's fallacy to me: imagining that the unlikelihood of events up until now happening affects the probability of what is yet to come.
You're wrong. It is logically true, and provable, although I cannot render the proof offhand (maybe someone else can).
Let's put it into another context which may help. The space between 0 and 1 is finite. We can clearly delineate the start and end. Yet, in that finite space, there is an infinite number of real numbers. This is something like the "infinite bounces in finite time" trick. It's true that in the physical world there aren't an infinite number of bounces, because outside factors will interfere and stop the ball from bouncing prematurely. However, it is possible in pure logical terms.
The carriers aren't giving away shit for free. They are subsidizing the cost of the phone in exchange for a contractual obligation to buy their service for x amount of time, just like they do for every other phone, including the iPhone.
Interesting, I didn't know that you could get prepaid data plans now. Thanks for the info, gives me something to look into when my Verizon contract is up.
But the idiots who modded you informative should really have known better. Factually wrong statements are not informative and if you can't tell right from wrong, you shouldn't mod.
No one said anything about them not being able to tell right from wrong. They may have simply been misinformed. People are firmly convinced of the truth of things which are wrong all the time, you can't expect someone to go out and double-check everything just in case they happen to be wrong on this one.
Infinity gets weird as hell. I don't remember the exact proof, but in a calculus class in college, the professor posed this question for "fun": if you have a ball that recovers 9/10 (or whatever the figure was, it's been a while) of its height with every bounce, how long will it take it to come to a complete stop? One of the students worked it out before the next class session, and we were all amazed to learn that even though the ball will make an infinite number of bounces, it will do so within 30 seconds. So an infinite number of actions can, theoretically, be performed in a finite amount of time. Pretty crazy, but the math was sound.
How? The probability of you picking the right door on the first try was 1/100, but now there are 98 doors taken out of the picture. Now there are two doors. The probability that yours is the right one is 1/2. The probability that the other one is the right one is 1/2. I fail to see how there is a better choice in this problem.
Infinity is not a number, you can't perform operations on it. You can, however, perform operations on a number which has an infinitely long decimal expression. So yeah, 9.999... -.999... is 9.0.
The guy in TFA sounds full of shit too. Honestly, it just comes off to me as a guy who's bitter that he's getting let go, and taking the opportunity to blast people who he didn't like.
Maybe there's truth to it. I don't know. But I sure as hell stopped reading about halfway through because with so many personal digs, it destroys his credibility in my eyes.
Exactly. If the FCC is going to try to regulate the carriers, why don't they attack the real problem? This middle approach TFS mentions is unsatisfying both to people who oppose government regulation of private business, and to people who want to be protected from getting screwed. It's even unsatisfying for the carriers. Everybody loses!
No, we have the presumption of innocence that says that he is a law-abiding citizen. If the FBI suspects he's not, they can gather evidence with due fucking process.
You know what the retarded thing is? The friend's comment that supposedly aroused suspicion is completely innocuous. All he's doing is pointing out how easy it is to attack the 99% of targets we haven't tried to harden, rather than the 1% we have, and concluding terrorism isn't much of a threat as a result.
Agree with his conclusions or disagree, it's hard to shake the idea that the FBI is punishing him because he had the nerve to think rationally, and point out how retarded our whole "anti-terrorism" thing is. How dare he see through the farce?!
Unfortunately, no it won't. It'll cause the general public, which is composed of idiots, to shake their heads at how awful those anonymous internet people are.
See, I can't agree there. I thought it got much better over the course of the game, and at its best was on par with all but the best FF games. And the combat system was a hell of a lot of fun.
I don't know about perishing; it's far more likely that the owners simply wanted the next version and tossed the original aside. You're right that it's meant to be a fashion accessory rather than a lasting investment, though.
Missing the point. If Apple was truly as consumer-focused as their marketing claims, they would offer this service to their customers. This has nothing to do with bitching about the expensive-ass hardware (although that's a valid complaint), this is about making the reasonable request that world-class prices be backed by world-class service.
I don't really agree that FF6 is as good as it gets held up to be. The story is kind of weak overall, and there are certainly memorable characters... but there are also awful characters. Kefka is a completely one-dimensional character who somehow regularly gets held up as a good example of a villain? Yeah, right. Then you have shit like Ultros (who is just fucking annoying). For every Celes in the cast, there's a completely unmemorable Gau.
Yeah, it's a good game. It is possibly even a great game. But I don't think it's as good as it is commonly said to be. Then again, lots of FF6 fans will leverage similar complaints against FF7, which I consider to be the greatest game of all time. Personal preference, I guess.
Slashdot Mirror
They have to be. All doors were equally likely to contain the prize at the beginning (or so it is reasonable to assume), so all remaining doors are still equally likely to contain it now. The other doors are nonexistent once we know them to not have a prize.
It's simple probability. Upon knowing that the other doors are not winners, you cease to consider them (they are no longer options, unless you're acting irrationally). There are now two doors, and only one door can have a prize. Thus, the probability that yours has the door is 1/2.
It does change the odds, but not in the way you're saying. It does not change the odds of you having picked the correct ticket initially (that was still 1 in 60 million). It DOES change the odds that you currently hold the correct ticket (that is now 1 in 2, since you are now, having been given the choice to switch, making a new choice from a pool of two... unless you're dumb, and are willing to choose something you know will lose).
You (and others) are acting as if the other 59,999,998 tickets (or 98 doors) still matter. They do not matter any more, because they are not part of the pool of choices any more once you know they are not winners. This does not affect the odds of the original choice, but it does affect the odds of the new choice. You guys are repackaging the gambler's fallacy: saying that the unlikelihood of events up until now have a bearing on the likelihood of events in the future.
You are talking about a bouncing ball, that is a physical object. If it is going to bounce an infinite number of times, it will take an infinite amount of time because it will never stop, ever. Hence, infinite amount of bounces. Once you cede that the ball will stop bouncing, you have also ceded that it did not bounce an infinite amount of times.
No. It will take a finite amount of time. That does not change the fact that infinite actions can take place in that amount of time. It's important to remember that it is not merely the height of the bounce that shrinks, but also the time it takes to bounce that shrinks. Because the time for each action is approaching zero, infinite actions can happen in the finite amount of time.
The math may have involved infinity in the terms of as the number of bounces approaches infinity, but not an infinite amount of bounces.
Those are the same thing. If the number of bounces approaches infinity as t approaches 30 seconds, it means an infinite number of bounces happen in those 30 seconds. You're drawing a distinction that doesn't exist.
Of course it doesn't change the chance that you initially selected the wrong door... but that's not the point. The point is that now that you know there are only two doors which are unknown (all the others do not have a prize), you get to choose again: there are two doors, and either one may have the prize. If you pick the one you originally picked, the odds are exactly the same as if you pick the one you did not originally pick.
You are saying two things. You are saying that the chance you picked the right door is both 1/100 and 1/2.
No I'm not. Perhaps I was unclear in what I was saying. Let me try again. The probability, upon your initial choice, of picking the right door is 1/100. Now, eliminate 98 wrong doors. The probability that either of those two doors is correct is 1/2. Thus, even though the probability of you picking correctly initially was 1/100, you have made the choice. Now, keeping that door is a new choice out of a pool of 2. The original probability doesn't apply any more.
So yes, the probability that you have picked the right door from the start is 1/100 (or 1/3 in your example), however, when you decide whether to stay or switch between the two doors, it is a new choice, and the probability has to be considered independently. What you're saying sounds similar to the gambler's fallacy to me: imagining that the unlikelihood of events up until now happening affects the probability of what is yet to come.
You're wrong. It is logically true, and provable, although I cannot render the proof offhand (maybe someone else can).
Let's put it into another context which may help. The space between 0 and 1 is finite. We can clearly delineate the start and end. Yet, in that finite space, there is an infinite number of real numbers. This is something like the "infinite bounces in finite time" trick. It's true that in the physical world there aren't an infinite number of bounces, because outside factors will interfere and stop the ball from bouncing prematurely. However, it is possible in pure logical terms.
The carriers aren't giving away shit for free. They are subsidizing the cost of the phone in exchange for a contractual obligation to buy their service for x amount of time, just like they do for every other phone, including the iPhone.
Interesting, I didn't know that you could get prepaid data plans now. Thanks for the info, gives me something to look into when my Verizon contract is up.
But the idiots who modded you informative should really have known better. Factually wrong statements are not informative and if you can't tell right from wrong, you shouldn't mod.
No one said anything about them not being able to tell right from wrong. They may have simply been misinformed. People are firmly convinced of the truth of things which are wrong all the time, you can't expect someone to go out and double-check everything just in case they happen to be wrong on this one.
Infinity gets weird as hell. I don't remember the exact proof, but in a calculus class in college, the professor posed this question for "fun": if you have a ball that recovers 9/10 (or whatever the figure was, it's been a while) of its height with every bounce, how long will it take it to come to a complete stop? One of the students worked it out before the next class session, and we were all amazed to learn that even though the ball will make an infinite number of bounces, it will do so within 30 seconds. So an infinite number of actions can, theoretically, be performed in a finite amount of time. Pretty crazy, but the math was sound.
How? The probability of you picking the right door on the first try was 1/100, but now there are 98 doors taken out of the picture. Now there are two doors. The probability that yours is the right one is 1/2. The probability that the other one is the right one is 1/2. I fail to see how there is a better choice in this problem.
Infinity is not a number, you can't perform operations on it. You can, however, perform operations on a number which has an infinitely long decimal expression. So yeah, 9.999... - .999... is 9.0.
The guy in TFA sounds full of shit too. Honestly, it just comes off to me as a guy who's bitter that he's getting let go, and taking the opportunity to blast people who he didn't like.
Maybe there's truth to it. I don't know. But I sure as hell stopped reading about halfway through because with so many personal digs, it destroys his credibility in my eyes.
Who's your carrier?
Exactly. If the FCC is going to try to regulate the carriers, why don't they attack the real problem? This middle approach TFS mentions is unsatisfying both to people who oppose government regulation of private business, and to people who want to be protected from getting screwed. It's even unsatisfying for the carriers. Everybody loses!
No, we have the presumption of innocence that says that he is a law-abiding citizen. If the FBI suspects he's not, they can gather evidence with due fucking process.
You know what the retarded thing is? The friend's comment that supposedly aroused suspicion is completely innocuous. All he's doing is pointing out how easy it is to attack the 99% of targets we haven't tried to harden, rather than the 1% we have, and concluding terrorism isn't much of a threat as a result.
Agree with his conclusions or disagree, it's hard to shake the idea that the FBI is punishing him because he had the nerve to think rationally, and point out how retarded our whole "anti-terrorism" thing is. How dare he see through the farce?!
Unfortunately, no it won't. It'll cause the general public, which is composed of idiots, to shake their heads at how awful those anonymous internet people are.
That's OK. It gave me the delightful opportunity to decide whether to make a Spanish Inquisition joke or a Penny Arcade joke. ;)
So that's three things.
(On each hand. So, six things total.)
See, I can't agree there. I thought it got much better over the course of the game, and at its best was on par with all but the best FF games. And the combat system was a hell of a lot of fun.
I don't know about perishing; it's far more likely that the owners simply wanted the next version and tossed the original aside. You're right that it's meant to be a fashion accessory rather than a lasting investment, though.
Missing the point. If Apple was truly as consumer-focused as their marketing claims, they would offer this service to their customers. This has nothing to do with bitching about the expensive-ass hardware (although that's a valid complaint), this is about making the reasonable request that world-class prices be backed by world-class service.
I don't really agree that FF6 is as good as it gets held up to be. The story is kind of weak overall, and there are certainly memorable characters... but there are also awful characters. Kefka is a completely one-dimensional character who somehow regularly gets held up as a good example of a villain? Yeah, right. Then you have shit like Ultros (who is just fucking annoying). For every Celes in the cast, there's a completely unmemorable Gau.
Yeah, it's a good game. It is possibly even a great game. But I don't think it's as good as it is commonly said to be. Then again, lots of FF6 fans will leverage similar complaints against FF7, which I consider to be the greatest game of all time. Personal preference, I guess.