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There are essentially 2 variables

1. A time line that is infinite

2. Events that are unlikely to happen often but have a non zero probability of occurrence

Is it true that all events with a non zero probability will eventually occur given an infinite amount of time?

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ChineseBandit58

classic undefined problem.

You are asking what is infinity/infinity = undefined

Easy

Is this like the monkey hitting random keys being able to type Shakespeare given long enough time to type?

Lsupimp

Sudden, unexpected & horrific flashback to Philosophy 2010 at LSU.

Powerman

quote:

You are asking what is infinity/infinity

Not quite

thetempleowl

quote:

1. A time line that is infinite

2. Events that are unlikely to happen often but have a non zero probability of occurrence

Is it true that all events with a non zero probability will eventually occur given an infinite amount of time?

This is easy.

Infinite time and something that is extremely, extremely rare, but not of zero probability.

Well, since you yourself have stated that this has a non zero probability (meaning it has a chance of happening), and you have infinite time, than it will eventually happen.

There isn't a question of will it happen, the question is when will it happen.

TrueTiger

It kinda makes sense.

If I get infinite times to play the powerball, it stands to reason that I will eventually win.

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davesdawgs

quote:

Is this like the monkey hitting random keys being able to type Shakespeare given long enough time to type?

Yes, and given the script of a play by Shakespeare in hand, which is more likely: that it was designed intelligently or created at random by a monkey?

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Powerman

quote:

This is easy.

Infinite time and something that is extremely, extremely rare, but not of zero probability.

Well, since you yourself have stated that this has a non zero probability (meaning it has a chance of happening), and you have infinite time, than it will eventually happen.

There isn't a question of will it happen, the question is when will it happen.

Of course this is the correct answer and anyone who states otherwise should be burned at the stake.

The only way for the event to not occur is for it to actually have a zero probability assigned to it.

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lsutothetop

yes

suppose Event X has probability Y of occurring in one attempt.

probability of X = Y
probability of not-X = 1-Y

in two attempts:

probability of X twice = Y^2
probability of not-X = (1-Y)^2
probability of X once = 1 - Y^2 - (1-Y)^2
probability of X *at least once* = 1 - (1-Y)^2

in Z attempts:

probability of X Z times = Y^Z
probability of not-X = (1-Y)^Z
probability of X *at least once* = 1 - (1-Y)^Z

this last one is the one we need, because we can cleanly separate all possibilities into two groups: X happening at least once, and X never happening

so, we have 1 - (1-Y)^Z
per condition (1), Z goes to infinity
0 < 1-Y < 1, so as Z goes to infinity, (1-Y)^Z goes to 0

1 - (1-Y)^Z = 0.999...
0.999... = 1
1 - (1-Y)^Z = 1
probability of X *at least once* = 1 - (1-Y)^Z = 1

therefore we conclude that yes, given an infinite timeline, any event with a non-zero probability will eventually occur

EDIT: extending this a bit to cover one clause that might make some people confused

0.999... = 1

the classic proof of this is with 1/3

1/3 = 0.333...
1/3*3 = 1
0.333...*3 = 0.999...
0.999... = 1

This post was edited on 12/29 at 12:45 pm

Easy

quote:

This is easy.

Infinite time and something that is extremely, extremely rare, but not of zero probability.

Well, since you yourself have stated that this has a non zero probability (meaning it has a chance of happening), and you have infinite time, than it will eventually happen.

There isn't a question of will it happen, the question is when will it happen.

Not really. There's only the possibility that it could happen. Doesn't mean that it will. Obviously not everything that can possibly happen eventually happens. Some things never happen.

TrueTiger

quote:

lsutothetop

I was able to do it all in my head.

Na-na-na-na-na-nah

lsutothetop

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Powerman

quote:

Not really. There's only the possibility that it could happen. Doesn't mean that it will. Obviously not everything that can possibly happen eventually happens. Some things never happen.

I suppose if you look at it this way you can come up with an infinite amount of possibilities of things that could happen in theory so you really would be looking at an undefined problem.

But let's say it's something simple like the powerball example. If you have an infinite amount of times to play the powerball, will you eventually win it?

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Easy

quote:

therefore we conclude that yes, given an infinite timeline, any event with a non-zero probability will eventually occur

So my aunt that never had kids before she died will someday actually have kids even though she's already dead?

Powerman

quote:

So my aunt that never had kids before she died will someday actually have kids even though she's already dead?

Wouldn't you assign a zero probability to that event though?

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lsutothetop

quote:

So my aunt that never had kids before she died will someday actually have kids even though she's already dead?

a dead person has probability zero of having kids

your aunt, when she was alive, did not have infinite time for the event of her having kids to occur

lsutothetop

can of worms time

does this have to do with the megathread about evolution? because I haven't opened it, but I can already envision people arguing that certain biological traits (human eye, human brain) are "too complex" to have evolved naturally and this question would directly pertain to it

Powerman

quote:

Yes

I always here that it's "severely unlikely" that X could happen.

Well I contend that when you're dealing with a few billion years a lot of things that are very abnormal and rare become more and more likely to occur.

TrueTiger

quote:

There's only the possibility that it could happen

I see what you are saying.

So time is a constantly changing variable and with each tick it increases the probability of a given possibility occurring.

You're saying that eventually the time will get the probability up to 99.99999999999999999999% but that the next tick may only add another 9 instead of a 100 and so, even given infinite ticks of the clock, we can still have infinite additions of 9.