**Quantum**:

Oh, don't worry about it, I wasn't offended at all, just thought I should make sure that Miles Mathis got a fair shake. :)

We should try going through his articles together (maybe you can create a thread, like you said).

And I honestly never pictured you as a redhead. XD

Just out of curiousity (and sorry if this is derailing your thread), but how do you picture me?

And congrats on getting to be in the mag. What's it for?

Cannot wait!! And that is NOT sarcasm XD really really

Yeah, congratulations, Jade. I'll have to read it some time.

I wish I could get into the magazine, but I haven't even submitted anything in a long time. :P

**Half.note: **Umm...blond. And while I'm doing this might as well throw in some other wild guesses:

5' 4"

Blue eyes

Anywhere close?

LOL, sorry. Couldn't be more wrong. XD

I have *brown* hair. *Brown* eyes. And I'm closer to 5' 9".

And my hair is reeeeeallllly long (like, past my waist long).

Not that it really matters. :P

Anyways, I should let you get to bed.

'Night.

Darn! I guess I'm not good at random guessing of physical features. "Night

Oh, and I don't know if this was the point of your thread, but the word "Probability" is in the title so I started thinking about it.

Today in science, our teacher told us that, based on probability, there are at least two kids in every class who have a birthday on the same day.

We tested this theory by going through everyone's birthday (and they discovered that it was my birthday yesterday so they forced me to stand on my chair while they sang happy birthday to me XD).

Anyways, there *where* two kids with the same birthday (and interestingly enough, the last two we asked).

Our science teacher said he would go through the math with us if we had the time, but we didn't end up doing it.

So I was wondering if you knew why this is.

I'm sort of curious now...

What do I think of Cayesian probability? Well, first off, I don't get it. At all. Send help.

As for the birthday probability thing, I don't know how to describe it mathematically with an equation or whatever, but I do know some of the logic. Ignoring seasonal effects, 9-months-after-valentines-day births, and leap years, imagine people are born on random days of the year.

For 2 people (obviously) this means a 1/365 probability, or about 0.274%. Not a lot. However, when you go to three people, you now have a system where any of the three people could share a birthday with either of the other two. Looking at this more in-depth,

The first person has a 1/365 chance to share a birthday with the firs person, and 1/365 to share with the second. This is where it's actually most easily expressed as probability to *not* share, and this means the probably can be expressed as (364/365)(364/365) or (364/365)^2.

The second has the same probability as the first to share a birthday, but wait! If the first does share a birthday with the second, we'd be counting that twice, once for each person! That's confusing. So doesn't it make sense that, instead of looking at individuals, we look at pairs of individual, since that's the scale on which the phenomenon takes place?

So let's do a re-take. In a group of three people, there are three possible pairs. So that's (364/365)^3, or 99.160% change to *not* share, or 0.840% to share.

With four people, there are 6 possible pairs, or (364/365)^6, or 1.633% to share.

But how do you figure out how many pairs are in a typical class of 25 students? Well, the first student could pair up with any of the 24 other students, so that's 24 pairs already. So could the second student, but wait! We've already accounted for the first and second pairing up, so that's down to 23. Ditto with the third, 24-2=22. Etc. So if we go all the way down, we get 24+23+22+21+20+19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1, until the very last student has already had all possible groupings accounted for. There's a shortcut for this which is, if x is the number of people in the overall group, (x^2 - x)/2. In this case, (25^2 - 25)/2 = 300.

Now we just need to apply what we did before, calculating (364/365)^2, it turns out there's a 56.091% chance for anyone to share a birthday! And with higher seasonal birth rates (more in the fall and such), the probability is even higher.

So there you go. You can calculate the same way for a system of any size.

Sorry for the marathon-length post, I just get really excited about math and statisitcs and probability.

So the Bayesian way of thinking about probability is as "an abstract concept, a quantity that we assign theoretically, for the purpose of representing a state of knowledge, or that we calculate from previously assigned probabilities," This is instead of the typical definition as a measure of frequency. This kind of probability can be treated objectively, but also subjectively by bringing in personal value judgments on the probability and thinking of probability as a personal belief rather than a real thing. Also, unlike frequentist probabilities, the probabilities change with new information.

Also, from wikipedia,

"For the frequentist a hypothesis is a proposition (which must be either true or false), so that the frequentist probability of a hypothesis is either one or zero. In Bayesian statistics, a probability can be assigned to a hypothesis that can differ from 0 or 1 if the true value is uncertain."

(remind anyone of quantum mechanics)