Probability question.

Originally posted by lausey
Also, abiogenesis. 😉

I don't think we know how probable that is. There are two many factors involved and all we really have is one example.
We don't even know whether or not it has happened more than once on earth. It might be happening regularly all over the place, just going unnoticed.

Originally posted by Palynka
You're correct in that one has to specify a distribution, but adam's point was that any distribution over a continuous support will give you individual draws of probability zero.

And the fact that most people will pick a rational number should tell us that the probability is not zero, therefore it is not a normal distribution (I had to look up what that meant - probability is not something I did much of at University.).

Originally posted by twhitehead
And the fact that most people will pick a rational number should tell us that the probability is not zero, therefore it is not a normal distribution (I had to look up what that meant - probability is not something I did much of at University.).

Yes, I said that. And? That doesn't deter that the bell curve (normal distribution) is a pretty standard distribution in nature (technically this is a result of the central limit theorem). And it is continuous which implies any draws from it are probability zero events.

Originally posted by Palynka
Yes, I said that. And? That doesn't deter that the bell curve (normal distribution) is a pretty standard distribution in nature (technically this is a result of the central limit theorem). And it is continuous which implies any draws from it are probability zero events.

I must have misunderstood you.
I agree that there are many events (if not most) in nature that are probability zero.

Originally posted by twhitehead
I intended it to be a definition of what I meant by random in that instance, not in every usage of the word.
I do realize that you may get the same result for other types of randomness, but I still maintain that your calculation assumes my definition.

[b]No it doesn't. And I'd like to know where do you get this idea from. All it assumes are very stand ...[text shortened]... le and I think it'd be good for you to read it.
I don't understand your explanation.[/b]

I am afraid I haven't studied measure theory or real analysis.

That much I had already guessed. And I'm pretty sure that you have studied real analysis too. Just like I'm also sure that you have studied Probability and Statistics on college and all of this was explained to you at that time

Could you explain what this standard result is and what it does assume?

It is just the statement of Cantor's diagonal argument in the language of probability.

Clearly it does assume that a highly biased selection (such as people) is being used, so there are assumptions. How does it define those assumptions?

No it doesn't. This result is proven without any mention of any sample.
Just get rid of the frequency interpretation of probability and things will be a lot easier.
Again probability is a mathematical function that is calculated resorting to integrals.

Originally posted by Agerg
More counter intuitive to me is the fact that the set of even numbers is equal in size to the set of integers.

😲😲😲

Now that is counter-intuitive!

😲😲😲

hey I bet Mandelbot can solve this!

Originally posted by adam warlock
No it doesn't. This result is proven without any mention of any sample.
Just get rid of the frequency interpretation of probability and things will be a lot easier.
Again probability is a mathematical [b]function that is calculated resorting to integrals.[/b]

Well then we are clearly talking about two different definitions of 'probability'.
What I fail to see is how your definition is any way relevant to the example given.
If I ask "what is the probability that a human being, asked to pick a number off the real number line selects a rational number?" and you answer "zero" then I would say you are wrong. Its actually very nearly 1.

Originally posted by twhitehead
Well then we are clearly talking about two different definitions of 'probability'.
What I fail to see is how your definition is any way relevant to the example given.
If I ask "what is the probability that a human being, asked to pick a number off the real number line selects a rational number?" and you answer "zero" then I would say you are wrong. Its actually very nearly 1.

Well then we are clearly talking about two different definitions of 'probability'.

Obviously!
And it is also obvious that you still don't know what probability is and it would do you wonders for to realize what probability really is.

What I fail to see is how your definition is any way relevant to the example given.

It isn't my definition: it is everybody that knows what they're talking about definition. Simple as that.

If I ask "what is the probability that a human being, asked to pick a number off the real number line selects a rational number?"

I can only say that that wasn't my question. The person who was talking to perfectly understood my question and I suspect that only reason you're ailing to grasp what I said is because you don't what you're talking about.

First I talked about the probability of getting a rational number or an irrational number and then I juxtaposed that result with an actual experience with actual humans and said that the results wouldn't be as predicted.
I did this for two reasons: to talk about the fact that there infinitely more irrational numbers than rational numbers. And to "show" that 0 probability events do happen.

I find it appalling that you learned all of this in college and yet you show no modicum of understanding of these trivial results of probability. I really do.

To finish it off here are some quotes from me. Read them care and maybe, just maybe you'll get them.

The probability of choosing a rational number is 0, yet almost everybody chooses a rational number when confronted with this question.
...
To make matters worse the probability of choosing an irrational number is 1 and yet just go around and ask this question to 100 people and see how many of them choose an irrational number as answer...

🙂

Originally posted by adam warlock
Obviously!
And it is also obvious that you still don't know what probability is and it would do you wonders for to realize what probability really is.

I find that hard to believe.
Can you give me a link to a fairly simple explanation?

It isn't my definition: it is everybody that knows what they're talking about definition. Simple as that.
No, it is not that simple. Definitions are not owned by anyone and I do know what I am talking about. I am simply not talking about what you are talking about, hence we have different definitions.

First I talked about the probability of getting a rational number or an irrational number and then I juxtaposed that result with an actual experience with actual humans and said that the results wouldn't be as predicted.
I did this for two reasons: to talk about the fact that there infinitely more irrational numbers than rational numbers. And to "show" that 0 probability events do happen.
Well then it was a badly thought out example, because it does not demonstrate a probability zero event happening. I still dispute your claim that a human being selecting a rational number is a probability zero event.

I find it appalling that you learned all of this in college and yet you show no modicum of understanding of these trivial results of probability.
I didn't learn all that in college. I have a bachelors degree in Mathematics(Major) with Computer Science (Minor). We had no courses specifically on probability as far as I recall.

To finish it off here are some quotes from me. Read them care and maybe, just maybe you'll get them.

The probability of choosing a rational number is 0, [b]yet almost everybody chooses a rational number when confronted with this question.
...
To make matters worse the probability of choosing an irrational number is 1 and yet just go around and ask this question to 100 people and see how many of them choose an irrational number as answer...

[/b]
And I dispute your understanding of the phrase 'the probability of choosing'. To clarify, what do you calculate the probability of choosing a 6 from a die to be? Would you give the same answer if it was a weighted die, and we were talking about throwing it?

I must admit, it's difficult to follow exactly what you're both arguing about 🙂. Bringing "what humans would choose when asked" into the discussion is a bit of a red herring, though. Humans clearly don't choose from a well-behaved probability distribution. Therefore comparing what they do with a theoretical result about well-behaved distributions is pointless.

More mechanical process such as "where exactly will this dart land" are a better example.

Originally posted by twhitehead
I find that hard to believe.
Can you give me a link to a fairly simple explanation?

[b]It isn't my definition: it is everybody that knows what they're talking about definition. Simple as that.
No, it is not that simple. Definitions are not owned by anyone and I do know what I am talking about. I am simply not talking about what you are ta u give the same answer if it was a weighted die, and we were talking about throwing it?[/b]

Dear God you really don't get it!!! And on top of that it looks like you really don't know how to read.

No, it is not that simple. Definitions are not owned by anyone and I do know what I am talking about. I am simply not talking about what you are talking about, hence we have different definitions.

Actually when one is talking in technical jargon definitions are owned by the people active in that activity. 🙂
This is Mathematics and on Mathematics probability has a well defined meaning.
If you use your own half-baked definition of probability that's your problem.

I still dispute your claim that a human being selecting a rational number is a probability zero event.

The fact that I claimed virtually the opposite of that hasn't still hit you in the head? Do you really think that I claimed that or are you just taking the pi$$?

I have a bachelors degree in Mathematics(Major) with Computer Science (Minor). We had no courses specifically on probability as far as I recall.

Ridiculous! Ridiculous! Ridiculous!

to clarify, what do you calculate the probability of choosing a 6 from a die to be? Would you give the same answer if it was a weighted die, and we were talking about throwing it?

Irrelevant.

Just read what I wrote please...

(I have a sneaking suspicion that you're no longer really disagreeing about anything, but haven't realised it yet).

Originally posted by mtthw
Humans clearly don't choose from a well-behaved probability distribution. Therefore comparing what they do with a theoretical result about well-behaved distributions is pointless.

Thank you!

Edit: I suspect that if he was remotely familiar with the actual definition of probability as a function and not as a fraction between favorable cases and the totality of cases, and the result of Cantor's diagonal argument he would realize that we we are indeed agreeing in a lot of things.

But everyone now and again he just likes to disagree with me and then come out as not being familiar with what he's talking about but still having the feeling that I'm wrong.

Edit2: From my first post:

The probability of choosing a rational number is 0, yet almost everybody chooses a rational number when confronted with this question.

😉

Originally posted by twhitehead
I didn't learn all that in college. I have a bachelors degree in Mathematics(Major) with Computer Science (Minor). We had no courses specifically on probability as far as I recall.

I call bunkum. Doesn't matter whether on your part or on the part of the prof who signed your B.Math. If there was no probability course in it, you're not a B.Math., however much you may have a paper saying you are.
FFS, we did probability in high school!

Richard