How can the probability of an event be exactly 0 or 1? Why? Isn't

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>>9107791
>probability that my die with all sides painted 1 will roll a 1
>1
you done goofed muh boi

>>9107791
>suppose there is no event which occurs with probability 0
>pick an element from the set of events at random
>what is the probability that this event occurs with probablity 0?

>suppose there is no event which occurs with probability 1
>pick a random element from the set of events
>what is the probability the the event you picked does not occur with probability 1?

Q.E.D.


I invented this so no stealing and posting on arXiv >:^)

>>9107796
>Q.E.D
>not learning to spell Latin
Quod Erat Demonstrandum

>>9107791
Probability that OP will shitpost again
>1

>>9107791
These are literal axioms you're arguing against. Give up.

>>9107791
>infinitesimal
So 0?

>>9107791
>what's the probability of picking a positive number from the set {1,2}?

Are you retarded?

>>9107791
Probability of OP not being a fag = 0

>>9107816
To be fair, I think OP's thinking of """real life""" circumstances, like a com flip with a tiny chance that the coin will lands on its edge. He just didn't realize that constructed events like you just mentioned are perfectly real.

He's still retarded, though.

>>9107816
>>9107796

Okay, what about in ""reality"" though all of these cases are on paper. For example see "Sun Rise Problem"

https://en.wikipedia.org/wiki/Sunrise_problem

I know it's brainlet as fuck but I guess I'm also asking why is [math] P(E) \in [0,1] [/math] and not [math] P(E) \in (0,1) [/math]?

>>9107840
Okay sure, quantum events mean you can teleport randomly before the event is completed. But then you're asking a physics question, and we don't care about those levels of accuracy. To 10 significant digits, the probability of some events is 0 or 1. But yeah there's nothing that really happens never or every time. There's nothing interesting here

>>9107840
That's just how the maths is, it's your job when using probability theory to model your problem correctly.

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>>9107791
>infinitesimal

>>9107800
Autism

>>9107840
Much like how there are no perfect circles or straight line in real life those probabilities just represent some ideal situation that we can use to model the real world by.

>>9107791
[math] Pr(A \cup A^c)=1, Pr(A \cap A^c)=0 [/math]

>>9107794
lands on its edge :3
fractures mid roll :3

Flip a coin to find out P(B)

If B is heads then P(B) = .5

So the complement of B is anything other than flipping a head. It can be tails or it can disappear completely or do whatever it wants. Either way it is still .5 which .5 + .5 = 1

>>9107796
rekt

>>9107791
Okay, well the probability of an event occurring or not occurring in a real situation may never be exactly 1 or 0. Probabilities are determined by the knowledge the observer has of the system. If there is some random element that technically obscures the probability prediction, but has so small a contribution that it is below the precision of the observer's knowledge, and does not affect the system in a meaningful way, then why bother including it in a calculation (if you even could)?

Think along the lines of trillions of atoms, and one decides to behave differently for a picosecond, how does that affect the predictions for the system in any way? Trillions is being kind.

>>9107828
If you spin the coin and throw it on a flat surface with no fiddling (like making the surface highly adhesive) it is impossible for the coin to land on its side and stay on its side. The coin spins while it falls so if it hits the surface on the side it is impossible for the impact to absorb all that spin momentum and leave the coin stable in upright position. If the surface the coin lands on has cracks or is highly adhesive (with a very short glueing time) or similar other such hacks, then yes, it is possible for a coin to land on its side and stay like that.

OP doesn't only suck at math, he also sucks at physics.

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>>9107800

QVOD ERAT DEMONSTRANDVM*

Ftfy barbarian

>>9107791
>How can the probability of an event be exactly 0 or 1?

If you prove that the probability of something is happening is 1 then that shows that the experiment is deterministic, which means that you should not model it probabilistically.

>>9107794
>Quantum probability reconfigures the dice such that there are 2 dots on one of the sides, and it lands showing that side. xD

>>9108394
No, a it's possible for events with a probability of 1 to not happen.

>>9108522
Only in "continuous" probability but we all know real numbers don't exist.

>>9108522
>probability 1
>not happen
Lrn2probabilly

Probability is a measure of certainty., which obeys axioms which we thing are true. In this measure, some events cannot be assigned any probability except 0(or 1) without braking axioms.

If in real life probability is always in (0, 1). But you can say that when conditions of an experiment approach ideal, proability may approach 0 or 1.

>>9108543
The probability that a nondeterministic event happens in a finite sample space is never 0 or 1. It can only be 0 or 1 in a continuous sample space (what's the probability that if you pick a random real number you get exactly 2). And as we know, infinity does not exist.

>>9108572
I wont agree that infinities dont exist, they are just undetectable.

>>9108578
Infinities make sense in various contexts but in probability they don't.

For example consider the question I asked, what's the probability that if you pick a random real number you get exactly 2? How would you even set up a random real number generator. With a computer? Nope. There are actually many real numbers computers cannot generate. Heck, there are even integers that a computer cannot generate.

This question only makes sense if you first reduce the question to "If you pick a natural number at random what is the chance you get exactly 2" and then you use a sequence of probabilities that converges to 0. But does that make sense? Are probabilities sequences? Are they series? Not really.

>>9108586
Consider biased coin, such that you know nothing about the coin. You can say that the probability of heads is itself a real random variable with some continuous distribution nonzero form 0 to 1.
Then the probability of the "probability of heads =m" = 0 for any m in [0,1].

>>9107791
>Isn't there always an infinitesimal chance that it will/won't occur?
Which would be an event of measure 0 :^)

I have a coin heads and tails
A = {It lands on heads on the first flip or it does not land on heads on the first flip or it lands or it does not land or something happens or nothing happens}
I toss it, slowmotion midair the camera pans to it dramatically, my eyes are squinting as I try to determine the probability P(A)? It's 1.

>>9107791
>go to casino
>put all your moneys on #37
>....
>$$$ ?

>>9108618
What you did there can only be properly defined with limits so again, doesn't really REALLY exist.

>>9107806
This. Theres no reason to say that probabilities as such exist in the real world. Its a mental tool

>>9107791
Because it will or it won't?

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>>9107828
>I want """""""Real Life Examples""""""""

Fucking Brainlet.
If I have a set of 2 apples, what is the probability I will choose an apple.
Is that "Real Life " enough for you?

>>9107791
>Probability OP is a wise-ass brainlet
>1

>>9107791
>Probability OP decided challenging statistical laws was a good idea
>1

>>9109961
but isn't that built up on the assumption that you are in fact holding 2 apples with 100% certainty?

>>9109961
turns out they were pears, nerd

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>>9107806
But anon, you can't prove that these "axioms" are true, can you?

>>9107791
Depends on your interpretation of probability.

In a bayesian interpretation, you're certainly right - probabilities exist in the mind and, therefore, there is always an infinitesimal chance of something seemingly impossible happening. But that's merely a fact about your mind, not a fact about the world.