15 Oct 10
Originally posted by twhiteheadAnd there are also cases of events having zero probability and still they happen all the time.
There are also cases where things seem improbable to us, but are actually quite probable. For example in a group of 23 people or more, there is a more than 50% chance of two people sharing a birthday.
15 Oct 10
Originally posted by mtthwThis seems to be pretty interesting. If you ever get to find this article then please post a link to it.
There's a very good essay on this by Ian Stewart and Jack Cohen. Unfortunately I can't find a reference to it. But I remember one part where one of them had a bet that "a coincidence will occur" while walking through an airport in Sweden. They then bumped into someone they knew and hadn't see for ages.
15 Oct 10
Originally posted by adam warlockFound it:
This seems to be pretty interesting. If you ever get to find this article then please post a link to it.
http://www.newscientist.com/article/mg15721174.[WORD TOO LONG].html
You need a subscription to read the article though, I'm afraid.
15 Oct 10
Originally posted by FabianFnasWe already discussed this.
Example please.
The definition of the probability of an event rests on the notion of you having to integrate the probability density on a given interval. If you only integrate on a number the integral is trivially zero.
I'm, of course, assuming that the probability density function is well behaved.
15 Oct 10
Originally posted by mtthwThere a nice story by Borges about this. It revolves around a book in a library that contains an infinite number of pages. Hence, the chance of opening it on any page is infinitely small. Yet the book opens nonetheless.
Pick a random real number between 0 and 1.
(A bit artificial, but it demonstrates the principle)
Look up the mathematical concept of "almost surely"
15 Oct 10
Originally posted by adam warlockThose delinquent, ne'er-do-well, probability functions: it's vanishingly unlikely anything good will come of them.
We already discussed this.
The definition of the probability of an event rests on the notion of you having to integrate the probability density on a given interval. If you only integrate on a number the integral is trivially zero.
I'm, of course, assuming that the probability density function is well behaved.
15 Oct 10
Originally posted by adam warlockYes, we've discussed this before. In order to understand what you mean, I ask again.
We already discussed this.
The definition of the probability of an event rests on the notion of you having to integrate the probability density on a given interval. If you only integrate on a number the integral is trivially zero.
I'm, of course, assuming that the probability density function is well behaved.
Please give me an example from real life.
16 Oct 10
Originally posted by KazetNagorraYou mean, you measure a photon twice and the probability that it has (exactly) the same energy both times is zero, and yet it happens?
Measure a photon. What was the probability it had the energy you measured it to have before you measured it?
Can it also be so that you measure the temperature of an object and find it to be (exactly) to be pi degrees. A probability of zero, yet it happens that an object has that temp when you heat it from zero to 5 degrees? Have I got it right?
Sorry, I construct another thought experiment as I don't know if a photon has a constant temp for a while, or not, as a quantum effect.
16 Oct 10
Originally posted by FabianFnasAny kind of event whose sample space is continuous.
Yes, we've discussed this before. In order to understand what you mean, I ask again.
Please give me an example from real life.
I think that your problem in this question is that you may be too hanged up on the frequency definition of probability and aren't very used in thinking that probability is a function that arises from an integral. I may be wrong but I really think this is the problem here.
But anywhoo:
Choose any number on the real line.
The probability of choosing a rational number is 0, yet almost everybody chooses a rational number when confronted with this question.
Mind that I didn't say that the probability of choosing a particular number is 0. What I said is that the probability of choosing a whole set of numbers (and this set is infinite) is 0.
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...
16 Oct 10
Originally posted by adam warlockI would counter that probability also depends on the concept of randomness. So your example seems counter intuitive because the choices in question are not random. Whether this makes you claims wrong I am not certain, but you probably are.
But anywhoo:
Choose any number on the real line.
The probability of choosing a rational number is 0, yet almost everybody chooses a rational number when confronted with this question.
Mind that I didn't say that the probability of choosing a particular number is 0. What I said is that the probability of choosing a whole set of numbers (and this s ...[text shortened]... k this question to 100 people and see how many of them choose an irrational number as answer...