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/sci/ - Science & Math

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4511533 No.4511533 [Reply] [Original]

I throw a coin on an infinite plane, randomly.
It falls at the position P. What was the probability for it to fall on P?

You should be able to solve this.

>> No.4511541

1/infinity = 0

>> No.4511542

how far away is the plane, what angle can i throw it as, is gravity present, do i need to account for air resistance?

>> No.4511548

>>4511542
Making it harder than it has to be
its a probability question not physics

>> No.4511546

>random point
>continuum

You can't pick one.

>> No.4511550

>>4511548
then 0.

>> No.4511554
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4511554

Only makes sense to talk about probabilities bound by intervals.

>> No.4511555

What the fuck guys, can't you into math?

>it falls at the position P

Then the fucking probability is 100% becuz we already know were its fallen.

>> No.4511559
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4511559

>>4511546
I pick 1, randomly.

>> No.4511562

>>4511550
>>4511533
If the probability is 0 then it couldn't fall on P. And it did.

>> No.4511565
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4511565

>>4511555

>> No.4511567
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4511567

>>4511554
Then the interval [P, P]

>> No.4511570

>>4511562
the probability to say the good position BEFORE the throw is 0. the probability you said P before you knew it'll fall on P was 0.

>> No.4511571

if uniform repartition 0

>> No.4511573

50%, either it happens or it doesn't.

>> No.4511575

>>4511567

Lim (x ->inf) 1/x = 0. Talking about probabilities with infinity is pointless.

>> No.4511576

There will be a probability distribution based on the initial trajectory of the coin or at least based on the position from which it was thrown.

Otherwise, if it was thrown from a random point anywhere on an infinite plane, i.e. making it truly random, then P=0. Before you start in with your herpderp "but it's on an actual spot" faggotry, it seems that you don't fucking understand probability. It's about predicting something BEFORE IT FUCKING HAPPENS, you dickless winged faggot. There was absolutely no way to know where it would land randomly on an infinite plane.

>> No.4511577

I tried it at home. The answer is potato.

>> No.4511578

>>4511562
When you have infinite sets, 0% doesn't mean "impossible".

The chance of a randomly selected integer (out of ALL integers, uniform probability distribution) being 3 is 0%, but it's still possible.

>> No.4511579
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4511579

>>4511576

>> No.4511583

>>4511576
You're just rejecting the given problem statement, not answering it.

>> No.4511590

>>4511578
no actually IT IS impossible for a randomly selected integer to be 3. or any other integer , it may seems wrong, but if you think about it , it makes sens.

>> No.4511594

About 9000

>> No.4511598

>>4511590
You don't know what "impossible" means.

>> No.4511601

>>4511590
No, it's impossible for a randomly selected integer to be pi. Or apple. Or a bag of dicks.

>> No.4511603

>>4511598
no you.

>> No.4511604

>>4511576
So the probability for the coin to land on any point is 0?
You're basically saying that a coin can't land on an infinite plane.
>>4511590
And you're saying that we can't pick a number randomly.

Because the sum of 0 from zero to infinity is 0.
And it should be 1. Sum of probabilities.

>> No.4511607

event A occured
what is the probability that event A occured

# of events in which A occured: 1
total # of events: 1
P = 1/1 = 1

>> No.4511609

>>4511578
>out of ALL integers, uniform probability distribution
There is no uniform probability distribution on a countable infinite set.

>> No.4511610

Thread is over, guise. I answerd teh question. Teh fucking coin ALWAYS falls on position P. Any other position is impossible. Probability is 100%.

>> No.4511611

Uniform distribution on unbounded set doesn't make sens

>> No.4511619

>>4511604
You suck really hard at at this. There are non-empty measure-zero sets.

http://en.wikipedia.org/wiki/Almost_everywhere
http://en.wikipedia.org/wiki/Almost_never

>> No.4511617

>>4511604
>So the probability for the coin to land on any point is 0?
>You're basically saying that a coin can't land on an infinite plane.

Are you descended from the great Zeno?

>> No.4511621

>>4511604
Learn to fucking read.

You can't predict beforehand where it will land. The probability distribution is the same across the whole plane. Any point is as likely as any other. There are infinite choices. You have no chance of predicting where it will land before it is thrown. That's what 0 probability means.

Oh wait, highschoolfag, amirite?

>> No.4511622

>>4511611
You can define a uniform distribution on a unbounded set as long as the lebegue measure of this set is larger than 0 and smaller than infinity.

>> No.4511624

>>4511609
Citation? And would you have the same objection for uncountably infinite sets?

>> No.4511641

>>4511622
yeah you are actually right

>> No.4511650

>>4511604
>sum of 0 from zero to infinity is 0.
no, no its not. 0*infinity is undefined, not 0. in this case it gives 1.

>> No.4511653

>>4511554
this obviously

OP should finish highschool and come back to /sci/ when he's less of a retard

>> No.4511655

>>4511650
No, you moron. When you sum up 0, it remains zero, even in infinity.

>> No.4511660

>>4511655
It must be nice doing math were naive simplifications apply.

>> No.4511665

>>4511555
You used to be funnier.

>> No.4511668

>>4511655
How do you feel about trollpi? Is the infinite limit the same as what all the finite-term expansions would have you believe?

>> No.4511671

>>4511665
What the fuck? I'm serious, dude.

>> No.4511674

>>4511668
I don't get your point. Is that some absurd trolling strategy?

>> No.4511681
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4511681

>Mfw when 5% of sci understands limits.

>> No.4511687

All this probability-zero stuff is the result of forcing probabilities into the inappropriate framework of real numbers, which were developed for doing geometry. There's no good reason to use the same system of numbers for probability.

>> No.4511695

>>4511674
You're assuming that the infinite limit has all the same properties as finite-term truncations. Since the curve is 4 long at each step, surely the infinite limit has length 4 too! Nope. Doesn't necessarily follow.

But at this point, I should admit there's an issue with defining a probability distribution here, as another anon noted.
>>4511622

>> No.4511701

>>4511671

What WAS the probability. We did not know that it would fall on P.

>> No.4511702

>>4511687
>implying we shouldn't use the real numbers for probability
Go on...

>> No.4511703

>>4511695
I'm not assuming anything. My only post ITT was correcting you, because you claimed that summing up zeros can result in anything non-zero.

>> No.4511704

>>4511701
We fucking DO know. OP told us so. We have to assume it will always fall on P. Maybe P is magnetic and attracts the coin.

>> No.4511708
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4511708

>>4511655
Of course that's your contention. You're a first year highschool student. You just got finished reading some introductory algebra, just x and y probably. You're gonna be convinced of that until next month when you get to z, then you're gonna' be talking about how discrete sums over the set of integers are necessarily integers themselves no matter how far down the number line you go. That's gonna last until next year, you're gonna' be in here regurgitating some highschool teacher's notes, talking about ya know, the modulus arithmetic on natural number rings and how infinity doesn't have any meaning on the ring....

>> No.4511710

50/50

>> No.4511715

ITT: people who still don't get how integration works.
want to know a fun fact ? dx=0

>> No.4511716

>>4511708

0/10, you're not even trying.

>> No.4511720

>>4511715
What the fuck? We don't need any integration to solve OP's porblem.

>> No.4511721
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4511721

>>4511619
I read your links and they're just dodging the problem of this thread.
Same thing for people who say "it's not allowed", "we can't pick a random point", or "it has to be an interval".
These are all arbitrary rules with no demonstration or logic behind them.
They exist because of this problem. Because of infinity.

The problem is that infinity is not a logically sound concept and cannot exist.
And thus dealing with it messes with other good axioms and produces incoherence.
And we have to invent strange rules to fix the mess.

Even matter and time have to be discrete, or an arrow would never reach its target.

>> No.4511723

>>4511703
Is it possible to divide a portion of the real line into an infinite set of Lebesgue-measure-zero subsets? If so, you certainly can sum over an infinite set of measure-zero sets and get a nonzero answer. Might be an uncountably infinite set though, so "summing them all up" needs examination...

Put it this way. Pick a real number between 3 and 4. The chance of picking pi is 0, but it's not impossible.

>> No.4511729

>>4511721
>The problem is that infinity is not a logically sound concept and cannot exist.
LOL Zeno, you so funny.

>> No.4511730

>>4511723
You are addressing the wrong guy. That's not what I was talking about.

>> No.4511734

It's 0. But it's not 0 from the empty set. It's just 0. Assume an uniform distribution on the infinite plane. Then the probability is lim n->infinity 1/n
which equals 0. But again, that doesn't mean it's impossible with the 0 you learn in basic probability.

>> No.4511732

>>4511721
I don't know about you, but calculus works just fine for me. I can even show you infinite sums of stricly-positive terms that add up to a finite number. I can even tell you what the answer is!

>> No.4511752

>>4511720
I think he is probably talking about the " probability 0 for every points => probability 0 for the whole set because sum of probabilities" argument. every integral is a (continuous) sum of zeros like <span class="math"> \int_{ 0 }^{1 } dx=1 \neq 0 [/spoiler]

>> No.4511755

>>4511752
Calling it a "sum of zeros" is mathematically incorrect.

>> No.4511763

>>4511533

>It falls at the position P.

>What was the probability for it to fall on P?

>What was the probability

Half of all hundred of the percents.

Coins only have two sides.

/thread.

Unless it falls in the middle.

>> No.4511765

>>4511702
I'm not sure exactly what set of numbers we ought to use for probability, but one desideratum would be the ability to sum over uncountable sets of nonzero numbers and obtain a finite result. See

http://planetmath.org/encyclopedia/UncountableSumsOfPositiveNumbers.html

for why this doesn't work for real numbers. Note that it depends on the Archimedean property, so there's hope that with a different system of numbers we wouldn't have this problem.

>> No.4511771

P(P)-->0

>> No.4511780

>>4511732
>I can even show you infinite sums of stricly-positive terms that add up to a finite number.
It only works because of the 1/inf=0 approximation and the like.
Which have been invented to deal with the mess.

Here is an example:
http://en.wikipedia.org/wiki/Geometric_series#Formula
Demonstration of the finite sum of an infinite series (which shouldn't be possible)
>As n goes to infinity, the absolute value of r must be less than one for the series to converge. The sum then becomes
And they then simplify 1 - R^n to 1. Because R^n -> 0 when n -> inf. They approximate.
And thanks to this they can calculate the finite sum of an infinite terms.
This is circular reasoning.

>> No.4511785

>>4511780
Now THIS is trolling.

Well done.

>> No.4511799

>>4511780
0.9+0.09+0.009+0.0009+....
every term is strictly positif therefor 0.999...= <span class="math"> \infty \neq 1 [/spoiler]

>> No.4511805

>>4511785
Multiplications are additions.
So using infinite product convergence to prove a finite sum is circular reasoning.

>>4511799
Yeah 0.999... = 1 is another misconception.

>> No.4511809

How fast is the plane moving? What altitude? How many passengers on-board?

>> No.4511811

1 mother fucker.

>> No.4511812

1/infinity

this isn't hard.

>> No.4511832

>>4511811

bitches don't know bout dat borel-cantelli lemma.

or dat measure theory.

>> No.4511836

>>4511812
no , the answer is 0 or lim 1/x when x go to infinity , but in no way it is 1/infinity which is not defined

>> No.4511854

>>4511836
The answer to the problem is undefined too... Coincidence?

>> No.4511870

uncountably infinite probability spaces don't make sense.

>> No.4511882

>>4511870

sure they do, just use integrals. As long as you talk about "probability to fall within a certain range x" then you're fine.