Question

If the probability of an event is non zero , does this mean the event Will happen in all time?

Answer 1

No. It won't. For example the probability is 1/2, we know that it is non-zero, but it doesn't happen all the times. Tossing a coin is an example. You wouldn't always get heads or always tails. Hope that helps :)

Answer 2

all the time*

Answer 3

but if you kept flipping it , for eternity, surely for some interval of time you would be on a streak of 10 000 000 heads ,
and also at another interval a streak of 10 000 000 tails

Answer 4

But, at least once(suppose), if you get a tail or a head and infinite heads or tails, that'd just mean that it's not happening all the time.

Answer 5

There is a slight of slightest chance for getting only a head or only a tail. But this doesn't mean that it WILL HAPPEN ALL THE TIME. It may, but WILL is the WRONG TERM we're using.

Answer 6

If you'd asked, "If the probability of an event is non zero , does this mean the event may happen in all time?", I'd have said yes.

Answer 7

i suppose your right it can only be one permutation at a time,

Answer 8

SO things that are improbably might or might not ever occur

Answer 9

If things are improbable then they'll never occur. For example: You put 2 red cards in a box. What is the probability of a green card to come out? Of course zero :D

Answer 10

i dident say impossible i said improbable

Answer 11

The probability of that is still 0 though. Isn't the question more like if you had 10 billion red cards and 1 green card if you kept going would you get a green card?

Answer 12

@ItsPerpetual It has a non-zero probability. 1/billion

Answer 13

@UnkleRhaukus Improbable and impossible are the same in the terms of math

Answer 14

yeah if you kept re shuffling the deck of 10 billion red and 1 green could you pull out 80 green cards in successive draws

Answer 15

Improbable mean unlikely

Answer 16

In math, improbable is impossible

Answer 17

That is simply not true please check your sources

Answer 18

I really don't see why it would be...
Unlikely doesn't mean impossible and there's no reason to change it just because you're using numbers as probabilities to look at thigns surely?

Answer 19

Alright. I gave the answer to the original question. Can I have a medal now(your choice)

Answer 20

Is the original question; given an event with a non-zero probability and an infinite amount of chances for it to happen, is the event guaranteed to happen?

Answer 21

That is exactly what i am asking

Answer 22

and i seam to be coming to the conclusion the answer is NO

Answer 23

it will happen...given enough time (for an event with non-zero probability)

Answer 24

Zarkon say it is guaranteed to happen,

now im confused again

Answer 25

Zarkon is right. If the probability is greater than zero, then with repeated tests, the event will happen.

Answer 26

Also, for any sequence of events, if that sequence of events has a non-zero probability of occuring, then with repeated tests the sequence will eventually occur.

Answer 27

@scarydoor What do you mean by 'sequence will eventually occur'

Answer 28

Think of it like this, maybe: if the probability of an event a is very small, then the event that a does not occur is 1-Pr(a). Pr(a)>0, so 1-Pr(a)<1. Say 1-Pr(a) = 1/5000 or something. For a to not occur given two tests has probability (1/5000)^2. With three tests, for a not to occur has probability (1/5000)^3, etc... you can see that the probability get increasingly closer to zero... the limit actually gets to zero, and it says that the probability of a eventually occuring is 1. There are some theorems you use in there, but I've forgotten their names...

Answer 29

so like in the decimal approximation of pi there is some interval where there are twelve zeroes in a row
\[\pi=3.14....~\dots~...000000000000... \dots\]

Answer 30

@Zarkon I mean that, say there is a random variable X which takes values a,b,c with certain probabilities. Say you take a value of X, then take another, etc etc... so you'll have some kind of sequence of values, maybe something like (a,b,a,a,a,a,b,c,c,a,a,....) etc.... I meant to say before that you can pick any finite sequence of combinations a,b,c and eventually you'll find somewhere in that sequence the one you want. I mean eventually as in if you continue adding values X to the sequence for an infinite length of time. That's what's usually meant by "eventually" I think.

Answer 31

@UnkleRhaukus that depends if the digits of pi are random or not... I don't think that you could say they actually are (although I'm not sure of the subtleties there...). For example, the first digit after the decimal place is 1... can you say that the fact that 1 is there is the result of a random variable which randomly chose 1, where all the other 9 digits had equal chance of taking that place? I don't think you can... but.... I'm not sure what's going on behind pi, myself.... there may be an alternate explanation that says you're right.

Answer 32

ok...It is possible to make a sequence that will not guarantee to have the outcome you want with positive probability. The way you described your sequence is ok though

Answer 33

im not heaps certain with pi either , but i know it goes on infinitely and never repeats

Answer 34

Again with the "sequence will eventually occur" question. It's quite similar to the quesiton of whether one outcome from the sample space will eventually occur, even if it has small probability. Think of it like this: instead of thinking of one event as being the random variable, you think about the sequence of say, 10 events in a row as being the random variable. There are different possible sequences you can end up with and they each have a probability. So then it becomes pretty similar...

Answer 35

does that mean it has every possible finite sequence included in it

Answer 36

@Zarkon I believe you are wrong. If I pick any arbitrary sequence of heads and tails, of finite length, then if I flip the coin for an infinite number of times, my sequence will eventually turn up, provided my sequence has a non zero possibility of occuring.

Answer 37

I am not wrong :)

the sequence I'm thinking of has decreasing probabilities for a specific outsome (sitll nonzero)

Answer 38

@UnkleRhaukus yes it does. Provided the sequence has a non zero possibility of occuring and is finite length. For example if the coin never lands on tails, then the sequence (tails, tails) will never occur... and with pi, since I'm not sure if you can apply random properties to that (I suspect you can't...) then I'm not really sure that that has every sequence of numbers in its decimal expansion...

Answer 39

@Zarkon what is the sequence you are thinking of?

Answer 40

suppose you flip a special coin that at roll n the probability of heads is (1/10)^n

even after an infinite number of flips you are not guaranteed to get a head even though the probability of success is positive at each flip

Answer 41

Ah, I suppose I should have mentioned that the random variable X is the same at each trial. You are producing a sequence from different random variables.

Answer 42

This talk of infinite events reminds me of the "Monkey typing Hamlet" thing. Anybody familiar with that?

Answer 43

I think so anyway. I skipped some of the earlier probability stuff.... so I'm a bit hazy on some parts of the insides of random variables... I think that if you change what the probabilities are, then you basically are defining a new random variable.

Answer 44

there is no requirement for a sequence of r.v.'s \(X_n\) to have the same distribution

Answer 45

Actually even with your changing random variable, the probability of never getting a head is 0...

Answer 46

At each flip, the probability of not getting a head is strictly less than one. Therefore, the probability of not getting a head after k flips is (1/m)^k where m is some value larger than one. (1/m)^k approaches zero as k approaches infinity. There are some subtleties that I'm glossing over... but that's basically an euler sequence I think. And all euler sequences converge in the real number space... it converges to zero.

Answer 47

I didn't say that it was a sequence of X_n, I said it was a sequence where you take a value from the random variable X repeatedly, implying that X is always the same.

Answer 48

I'll let you think about it.

Answer 49

"yes the limit of the sequence is zero". And the limit is defined as "the probability that you will never get a head. The probability that you will get a head is 1-probability that you will never get a head. You've agreed the probability you'll never get a head is 0, so the probability that you will eventually get a head is 1-0 = 1. That is to say that it is certain you will "eventually" get a head, even though it's increasingly improbable.

Probability is unintuitive sometimes.

Answer 50

Lol. You have a think about it too if you want.

Answer 51

this 'And the limit is defined as "the probability that you will never get a head.'

is not correct

Answer 52

I'll let you trhink about that.

Answer 53

Do you know what a euler sequence is? You seem to be misunderstanding everything I type, and now would like me to ponder your unawaredly confused state. No thanks.

Answer 54

I was going to say the same thing about you.

I typed above that what you had was fine...BUT, I wanted clarification of what you meant by sequence since it IS possible to make a sequence of r.v.'s that have the property I described.

you said I was wrong...when in fact I am not. I'm sorry you don't understand.

Answer 55

Ages ago you asked what I mean. I said this: "I mean that, say there is a random variable X which takes values a,b,c with certain probabilities. Say you take a value of X, then take another, etc etc... so you'll have some kind of sequence of values, maybe something like (a,b,a,a,a,a,b,c,c,a,a,....) etc.... I meant to say before that you can pick any finite sequence of combinations a,b,c and eventually you'll find somewhere in that sequence the one you want. I mean eventually as in if you continue adding values X to the sequence for an infinite length of time."

I clearly state that you have a random variable. "a" as in "one" and that you take values from that random variable... From that one. As in, unchanging. Any sane person would read that as though you have just the one random variable. It doesn't change. Then later you make some argument that I'm wrong by using a bunch of different random variables? I think you need to work on reading comprehension or something.

You're still wrong about your counter-example you created using your own wacky interpretation. So you need to think about that.

Answer 56

again...I'm sorry you don't understand

Answer 57

Well this question has been a success.

Answer 58

Zarkon I am sorry that you believe it is me who does not understand when I have just explicitly demonstrated that it is you. That takes something.

Answer 59

your both wrong the one who dosen't understand it me

Answer 60

Would you like more help @UnkleRhaukus ? I can attempt to explain some details more fully.

Answer 61

as I wrote above what you first wrote was correct...I was just pointing out that it is possible to have a sequence the way I described it...

you said I couldn't .

Answer 62

well, generally the assumption of meaning is "it's impossible to have that because I've stated that I'm working with these conditions in which that case is impossible...". Of course you can have a sequence of whatever you want if you ignore what restrictions had previously been described. If I had said "oh no, I didn't mean that this applies to sequences of automobiles, because I'm talking about random variables..." would you be wise to point out "you're wrong! Because I can come up with a sequence of automobiles!"....

Answer 63

you said that what I was doing could not be done when in fact it can

Answer 64

So your whole point was, that even though I said that my result is based on unchanging random variables, that you wanted to point out that I can in fact create a sequence of numbers which come from different random variables? If that is the case, then well done for pointing out the obvious.

Answer 65

the point I was making apparently was not obvious since you still don't get it...learn some probability and then come back...I'm done this this conversation.

Answer 66

Hey did you know that 2+3=11? No I don't care that we all agree on the rules of maths. I just want to show you that I can write that and it is correct in my number system. Becauase I have created a different number system now that I pull out every time someone says 2+3 is not equal to 11.

Answer 67

i can conclude
an event is guaranteed to happen given finite probability and infinity time

Answer 68

Almost: not finite probability, rather, non-zero probability.

Answer 69

I feel sorry for you scarydoor

Answer 70

thankyou for letting me know how you feel. Any purpose to that?

Answer 71

if you think i am breaking 'math rules'

'No I don't care that we all agree on the rules of maths.'


then you clearly lack understanding.

Answer 72

@Zarkon learn the meaning of analogy, because that is what I did above.

Answer 73

did you even learn the rules of probability is school?

Answer 74

Is is possible to have a two sided coin (heads/tail) and i flip it infinity many times .
Is there some chance the coin never shows a tails

Answer 75

If the tail has non-zero probability, then there is zero probability that it will never show tails.

Answer 76

assuming a distribution would suggest that the chance is zero , but why is it not Possible

Answer 77

Hey everyone, let's keep this debate on the positive side, eh?

Answer 78

Informally: Because you have an infinite amount of trials. There is always some small chance of getting a tails... eventually it occurs.

Answer 79

(clever people arguing is sign of a good question, )

Answer 80

maybe the infinities in my brain are too small

Answer 81

(Yes).....in theory (but you and everyone else might well be dead beforehand)

Answer 82

but slightly less informally, say the probability of the event not occuring is a. a < 1. The probability that the event doesn't happen after k trials is a^k. since a<1, a^k approaches zero as k approaches infinity. That's a result from analysis. So, the limit as k approaches infinity of a^k is zero. That is to say that with an infinite number of trials, the event not occuring has probability zero. That is to say it is impossible for the event to not occur.

Answer 83

estidier i would probably give u after 145 goes anyway

Answer 84

:-)

Answer 85

2^70 should take care of most things, more bits than the observable universe....

Answer 86

im not about to measure the spin of ever single nucleon
if i get 145 heads in arrow the chances are \[2.2 \times 10^{-44}\] slim

Answer 87

if the chances are positive that something will occur , will it necessarily occur twice in infinite time

Answer 88

will it occur infinite number of times, a smaller infinity of course

Answer 89

Yes. You could think about it in a few ways. One way: you will get the value at least once, eventually. After that, you still have an infinite sequence... and it's really no different. So it'll come up again. So actually it'll occur an infinite amount of time... given enough time...

Answer 90

yeah there are infinities buried in the larger infinity

Answer 91

Actually the sizes of the infinity are the same I think. They can both be mapped onto the natural numbers, which is... countably infinite.

Answer 92

in the right ratio

Answer 93

if they were the same then the event would occur every time

Answer 94

Basically, just take the first occurence... map it to the number 1. Take the second occurence, map it to the number 2, then keep going... So that is kind of intuitively what is meant when saying that something is countably infinite.

Answer 95

No, it's how infinity is measure. It's not saying they have exactly the same number of elements, but that the type of infinity of them are similar... I thought that's what you meant when you said they are different kinds of infinity. Generally you only really compare infinities in terms of their similarity to a few different kinds of sets of numbers.

So, for example, the positive integers, and the even positive integers, are said to have the same type of infinite size... However, the real numbers have a larger infinite size than those two...

Answer 96

But yeah, the sequence of all random numbers will have elements that aren't fuond when you gather together only certain events chosen from that sequence.

Answer 97

and irrational numbers have greater density than both right?