# Statistics conceptual questions

Hi all

I took a course subject in basic statistics but its been so long ago I find that I have mixed up or forgotten some of the concepts so I hope someone here can help me refresh my memory.

1) Probability starts from 0 to 1, you can have any range of numbers but they cannot exceed 1 or be less than 0 (true/false)

2) If you have a probability of greater than 0, regardless how small that probability is it will occur given enough time (say infinite amount of time)

3) I was intrigued by a poster with a list of "facts" that supports creationism, it mention someone about Borel and his law and something about infinite monkeys. I did my google but I am still not a 100% sure of what I am reading so I am simplifying my statements here

a) Borel law simply states that if you have a small probability, the probability of it occuring is almost negligible
b) If you have a monkey typing for infinity, then the chance of the monkey typing out Hamlet is almost certain

Thanks!

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HallsofIvy
Homework Helper
Hi all

I took a course subject in basic statistics but its been so long ago I find that I have mixed up or forgotten some of the concepts so I hope someone here can help me refresh my memory.

1) Probability starts from 0 to 1, you can have any range of numbers but they cannot exceed 1 or be less than 0 (true/false)
I'm not sure what you mean by "any range of numbers" but, yes, a "probability" cannot be less than 0 nor larger than 1.

2) If you have a probability of greater than 0, regardless how small that probability is it will occur given enough time (say infinite amount of time)
No, that is not true. You can never say something will happen in probability.

3) I was intrigued by a poster with a list of "facts" that supports creationism, it mention someone about Borel and his law and something about infinite monkeys. I did my google but I am still not a 100% sure of what I am reading so I am simplifying my statements here

a) Borel law simply states that if you have a small probability, the probability of it occuring is almost negligible
Actually, "Borel's Law" does not say that- that's just directly from the definition of probability. "Borel's Law" (not really a law in the mathematical sense, just a "rule of thumb") says that you can find a "cut off" so that events with probability less than that cut off number can't reallistically happen under whatever conditons you have set (length of time you are letting the "experiment" run, etc.). Of course, that "cut off" will depend upon the additional conditions you have set.

b) If you have a monkey typing for infinity, then the chance of the monkey typing out Hamlet is almost certain
Theoretically yes. But other than "theoretically" the situaltion is meaningless.

Thanks!
http://www.talkorigins.org/faqs/abioprob/borelfaq.html
which points out that the "creationist" argument based on "Borel's Law" tend to ignore the non-random determinants in evolution- exactly the things that Darwin's argument was based on. Creationists typically see no intermediate position between "determined by God" and "completely random".

I'm not sure what you mean by "any range of numbers" but, yes, a "probability" cannot be less than 0 nor larger than 1.
I meant any range of numbers between 0 and 1

No, that is not true. You can never say something will happen in probability.
so if say the probability of a chimpanzee typing out the whole script of Hamlet is 0.000000000000000000000001 (you get the idea) but if the chimp has infinity time to do it, it WILL NEVER occur?

http://www.talkorigins.org/faqs/abioprob/borelfaq.html
which points out that the "creationist" argument based on "Borel's Law" tend to ignore the non-random determinants in evolution- exactly the things that Darwin's argument was based on. Creationists typically see no intermediate position between "determined by God" and "completely random".
What do you mean by non random determinants?

Thanks for your help, much appreciated!

HallsofIvy
Homework Helper
Originally Posted by HallsofIvy
No, that is not true. You can never say something will happen in probability.
so if say the probability of a chimpanzee typing out the whole script of Hamlet is 0.000000000000000000000001 (you get the idea) but if the chimp has infinity time to do it, it WILL NEVER occur?
No, I didn't say anything like that! Are you thinking that the only possibllities are "must happen" and "will never happen"? "Probable" and "possible" are quite different things. Given each letter equally likely, it is possible that, in an infinite string of letters you get "aaaaaa...", all a's. On the other hand, it is also possible that the letter "a" will never occur. Neither one "must" happen.

What do you mean by non random determinants?

Thanks for your help, much appreciated!
I mean, of course, natural selection which will weed out fatal mutations.

No, I didn't say anything like that! Are you thinking that the only possibllities are "must happen" and "will never happen"? "Probable" and "possible" are quite different things. Given each letter equally likely, it is possible that, in an infinite string of letters you get "aaaaaa...", all a's. On the other hand, it is also possible that the letter "a" will never occur. Neither one "must" happen.
In statistical terms, how would u define probable and possible?