Math Is Fun Forum

Fruityloop

Member

Registered: 2009-05-18

Posts: 143

Small probability = 0?

I remember reading somewhere that if the probability of an event occurring is too small, say 10^-50, then it is basically equal to zero.
In other words, it will never happen given even an infinite amount of time and trials.  That seems odd because you would think that
with an infinite amount of trials every event that could happen, will happen, no matter how small the probability.  But, let's say I ask you to keep flipping a coin until you get 1,000,000,000,000 heads in a row.  It seems that this will never happen no matter how long you try.  Maybe this explains part of the St. Petersberg paradox (which is discussed elsewhere on this site).  Thoughts anyone?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Small probability = 0?

with an infinite amount of trials every event that could happen, will happen, no matter how small the probability.

Yep! If we are not too concerned with the term "infinite amount of trials", whatever that means.

I think infinity is misused a lot in mathematics and this is the cause of much confusion. Zeilberger considers eliminating it. Check out Dieudonne's comments here https://vimeo.com/127338218 starting at 31:00.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: Small probability = 0?

Hi,
I do not know where you read that, but it sounds like a simplification for the sake of deriving some result. The chance of a trillion heads in a row has a very real probability. It Is 1/(2^10^12). This is such a ridiculously small number that I don't have access to an engine that can evaluate it. But it is not zero.

The way probability works is if the probability of an event is 10^-50, it will take an average of 10^50 events before it occurs

Last edited by Relentless (2016-02-05 21:28:58)

rileywkong

Member

Registered: 2016-05-26

Posts: 17

Re: Small probability = 0?

I once read somewhere that a probability less than 10^-150 is generally considered impossible. (At least within the [secular] time frame of the Universe.)

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Be nice.
"Life is like a bicycle; to keep your balance, you have to move." - Albert Einstein

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Small probability = 0?

I would say impossible is a bad word to use. It is just very unlikely.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Small probability = 0?

Impossible is a word to be found only in the dictionary of fools.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}