Aaron Davies turpitued:

I've heard people talk about "finite" probabilities before, when what ... is greater than zero i.e., that it can in fact happen.

Careful! "With probability zero" does not mean the same as "can never happen".

Why doesn't it?

Charles Riggs

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Aaron Davies turpitued: Careful! "With probability zero" does not mean the same as "can never happen".

Why doesn't it?

Evan's response to Peter went into the matter. It's a fallacious argument, of course.

Matti

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Ah // threads, // worlds. For an example, consider the ... that it can happen, since all the throws are independent.

Is it? One can construct a "probability space", modelling the tossing of a fair die infinitely many times, for which ... chance of tossing a 6 is 1/6) and (ii) it is impossible to not throw a 6 infinitely many times.

Only if the modelling is done incorrectly.

In the set of all infinite sequences of the form

{1,4,2,5,3,4,...}

there is an (uncountable even, but of measure zero) subsset of sequences that do not contain a 6.

Best,

Jan

Is it? One can construct a "probability space", modelling the ... is impossible to not throw a 6 infinitely many times.

Only if the modelling is done incorrectly. In the set of all infinite sequences of the form {1,4,2,5,3,4,...} there is an (uncountable even, but of measure zero) subsset of sequences that do not contain a 6.

And in the model I have in mind this set has been removed. One of the useful features of probability theory is the flexiblity one has in choosing a model.

J.

Nought point three recurring is not a finite number.

In addition to Evan's comments, the probability you seek is not 0.333..., it's 1/3, which is an exact representation.

But 1/3 = 0.333..

J.

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Nought point three recurring is not a finite number.

Thanks. Others have answered better than I could. The only infinite thing about it is the number of digits required to represent it in base

10 (and in infinitely many other bases).

Paul

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Bob Cunningham turpitued: The physicists are the ones who don't call it a quantum leap.

No physicists I know would use that "leap" part.

Nor would we chemists.

Paul

In bocca al Lupo!

Aaron Davies turpitued: Careful! "With probability zero" does not mean the same as "can never happen".

Why doesn't it?

Consider the example I gave in another reply:

throwing a die infinitely many times without a six coming up is possible (all throws being independent)

but it has probability zero.

Best,

Jan

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Only if the modelling is done incorrectly. In the set ... zero) subsset of sequences that do not contain a 6.

And in the model I have in mind this set has been removed. One of the useful features of probability theory is the flexiblity one has in choosing a model.

That you can do,

but then your model doesn't model independent throws with a die,

Jan

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