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Probabilities question by Lydia Honeycocke - Tue, 03 Jun 2014 04:31:49 EST ID:gxFYvDAi No.14058 Ignore Report Reply Quick Reply
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I'm far from any sort of math guy - so sorry for this probably basic question. I don't know how to say it, so I'll just say it

Is it actually possible to "concatenate" probabilities?

Like, they say if you flip a coin 100 times (let's say a perfect coin with a perfect flipper), you should expect to see it land on heads 50 times and land on tails 50 times. Or let's say you're playing pokemon; if you encounter 10000 pokemon you should expect at least 1 shiny (odds are ~1/8192 for non-nerds). Or so the conventional wisdom goes; in short, if you do something more than once, you should expect the probability of it happening a certain way to be multiplied by the unit chance.

I was playing an RPG the other day (well, shiny hunting to be exact) and it got me thinking.

So like say there's an RPG, and as you're going around for a particular monster has 10% encounter rate. You walk a path with exactly 10 encounter spots (and you aren't walking back because examples); hypothetically you could predict that you'll hit that particular monster once, right? That isn't to say you will or won't multiple of its kind, but you won't be surprised with one encounter, right?

So what happens if you're half way into that? The game "rolls the dice" every time you take a step; let's say you know how the game works and it doesn't employ counters or anything, it's just relying on a pretty advanced PRNG generator - it's as random as it gets. So there's no reason the previous five rolls should affect the next five, right?

So what happens if we look at the odds again? Well, the maths the same, but now we only have 5 chances to encounter that particular monster. So now our odds are 50%, right?
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Hamilton Gishstock - Tue, 03 Jun 2014 12:14:46 EST ID:SzH+rmP/ No.14059 Ignore Report Quick Reply
First off,

>you don't actually have a chance of tossing a coin 100 times and getting heads 50 of those times

Yes you do. In fact, you have an ~7.96% chance. Read this to learn why:


>Is it actually possible to "concatenate" probabilities?

Yes, this is called conditional probability. Bayes' theorem is typically used to find conditional probabilities. Read these:


Also, your interpretation of the Monty Hall problem is incorrect; the probability of winning after switching is 2/3 not 50%.
Albert Sicklekirk - Sun, 08 Jun 2014 22:18:09 EST ID:ik2IEAT/ No.14074 Ignore Report Quick Reply
You're combining two different ideas of probability.
Consider a coin flipping.
If you flip a coin five times, the probability of getting a heads the sixth time is 50% still.
However the probability of getting five heads in five flips BEFORE YOU FLIP ANY is 1/32.
So you see, you can expect a certain amount of a result in a certain amount of trials before you do the trials - this probability is different from the probability of a success or failure for each particular trial.

In your Pokemon example, if the probability of finding a caterpie I'm viridian forest is 1/10 but finding weedle is 9/10, then we can conclude the following:

Finding caterpie is 1/10 chance EACH TIME YOU ENCOUNTER SOMETHING
because the probability is 1/10, you can expect to see one caterpie AFTER TEN ENCOUNTERS (this is called the expected value)
Fanny Smallstock - Mon, 09 Jun 2014 02:07:28 EST ID:V2nhYpJ2 No.14075 Ignore Report Quick Reply
>you can expect to see one caterpie AFTER TEN ENCOUNTERS (this is called the expected value)
If by "you can expect" you mean "there is more than 50% change that", then this is true.
Actually the 50% change is passed after 7 tries. After the ten tries the propability is about 65%.
I wouldn't call myself that unlucky if I didn't hit the 65% chance. That's why I don't like to think in
expected values.

To calculate the propability of getting at least one occurrence that has a propability of p, when
trying n times, is
1 - (1-p)^n
In this case
1 - (1-0.1)^10 ~= 0.65
To get to 95% of getting a caterpie you need 29 tries.
1 - (1-0.1)^29 ~= 0.95

Am I doin it right? by Hamilton Goodville - Sat, 31 May 2014 17:02:28 EST ID:SMOxvvOF No.14052 Ignore Report Reply Quick Reply
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To prove: [(A∪B) = B] ↔ (A⊂B)

  1. Let A⊂S, let B⊂S
  2. Premise: (A⊂B)
  3. (x∈A) → (x∈B) [from 2]
  4. (A∪B) = B [from 3]
  5. (A⊂B) → [(A∪B) = B] [from 2,3,4]
  6. Premise: [(A∪B) = B]
  7. (x∈A) → (x∈B) [from 6]
  8. (A⊂B) [from 7]
  9. [(A∪B) = B] → (A⊂B)
10 . [(A∪B) = B] ↔ (A⊂B) [from 5, 9]

Is this proof even close to correct?
John Birryfoot - Sat, 31 May 2014 20:01:53 EST ID:3EegWVCd No.14053 Ignore Report Quick Reply
If you're doing this so formally, shouldn't you prove that the two sets are equal by showing that each is a subset of the other?
Reuben Sapperstod - Sun, 01 Jun 2014 03:01:49 EST ID:jEbtLayo No.14055 Ignore Report Quick Reply
How do you get 4 from 3? To show set equality you need to do as
DFENS - Sun, 08 Jun 2014 03:16:25 EST ID:S/NbzhXl No.14068 Ignore Report Quick Reply
He's proving that the statements are identical (i.e. proving a if and only if statement), not that A and B are the same sets...

I don't see anything incorrect with the proof.
Shit Humblewedge - Sun, 08 Jun 2014 19:26:53 EST ID:3EegWVCd No.14072 Ignore Report Quick Reply

He's proving that the statements are equivalent, that is different from them being identical. you should have read lines 3 and 4 of the proof....

Fitting a function to a dataset by Isabella Pittwill - Sun, 25 May 2014 01:06:07 EST ID:+KSmRNm9 No.14035 Ignore Report Reply Quick Reply
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For this function, I need to determine the constants B and k which make this function best fit a set of data points. The constant A is known and the data points correspond to the variables b and I, which are known.
Barnaby Nicklestock - Sun, 25 May 2014 10:52:05 EST ID:SzH+rmP/ No.14037 Ignore Report Quick Reply
Just input the values for f(b, I) and the corresponding values for b and I to make a system of equations. Then just solve the system of equations for B and k.
Augustus Bellystore - Tue, 03 Jun 2014 17:49:58 EST ID:eRJExMRq No.14061 Ignore Report Quick Reply
For a nonlinear fit like this you want to start from the statement that the best fit line will have constants such that the probability of having such a datasetis maximized. Write out the probabality of getting such a result if it's expectes to fit said model, then maximize it using Lagrange multipliers (usually rather than maximizing the whole function there will be some argument whose minima corresponds to the maxima of your probabolity )

I'm here to talk about math by George Homblefid - Thu, 22 May 2014 08:33:01 EST ID:vbUXvUHw No.14021 Ignore Report Reply Quick Reply
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These things are how nature tells itself how to be. And you are nature.

Arthur C Clark presents Fractals - Colors of Infinity.


this film, it's thought provoking, intellectually stimulating, virtually a comprehensive overview of fractal equations, graphs, and has interesting people and is psychedelic.

can't i discover a fractal equation graph for everything? cant' you? does anyone get how profound this is for science?
4 posts and 3 images omitted. Click Reply to view.
Edward Dallerwed - Sun, 25 May 2014 18:29:01 EST ID:Dk8yywxc No.14039 Ignore Report Quick Reply

Just iterations?

Sounds like you and the above poster don't like math at all. Most mathematics is just repeating the axioms and rules of productions of systems to obtain the results, if you think that applying a set of rules to obtain an interesting and aesthetically pleasing result is boring or trivial then math is not for you. The fact that the pure mathematical patterns are roughly paralleled in the physical universe is about as profound as it gets my friend.

To have abstract mathematical patterns realized in everything from lightning bolts, to ocean waves, crystals and river networks, is fascinating. In fact, finding these patterns in the real world suggests to me that they have more inherent basic meaning, or at least a reason behind their prevalence, than much of mathematics.


I don't know about an n-dimensional mandelbrot set but I do know that N-dimensional fractals exist, and in fact both countable and uncountably infinite dimensional fractals exist. You won't find pretty pictures of them for obvious reasons, but it is a simple matter to think of a Koch snowflake in many dimensions, for example.

Just as in instance of something non-broccoli related that has a lot to do with fractals, many ice melting patterns on the poles of mars have been found to exhibit fractal behavior
Hedda Docklebug - Mon, 26 May 2014 01:47:33 EST ID:sPd/0oB/ No.14043 Ignore Report Quick Reply
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>They aren't intelligent design or whatever your pet nonsense is, they're reiterations; sorta like loops. There's nothing profound about them.
I understand why a simple L-System like picture related can produce a tree or a leaf. It's not very complex, just reiterations and loops as you said. Even a plant can do it. You're actually designing the pattern, you can try it yourself: www.dangries.com/Flash/FractalMakerExp/FractalMaker_exp.html

But I've yet to understand why the Mandelbrot set emerge from OP's picture. It doesn't seem to be designed, as if Mandelbrot said "ok, take this pattern and reproduce it recursively and tweak it a bit". It's just a recursive sequence with a fucking square and that's it.

The formula itself isn't really interesting to be honest. The interesting part are the complex numbers, and especially complex multiplication. They're a really neatly designed piece of math. The Mandelbrot set and Euler's formula are great showcase of complex numbers and their possibilities.

>To have abstract mathematical patterns realized in everything from lightning bolts, to ocean waves, crystals and river networks, is fascinating.
Fractals are found everywhere because fractals are efficient patterns. If you're a plant and you're trying to maximize the surface to get more sun while minimizing the amount of material, you'll grow on a fractal pattern. Just like a bubble form into a sphere, because a bubble is trying to minimize the surface while maximizing the volume.
Yet sphere are not "more pure" or "more fondamental" than fractals. Math is everywhere in nature, and not everything is fractals: >>14022

>I don't know about an n-dimensional mandelbrot set
I mean a generalization of the mandelbrot set to N-dimensions. There are things like mandelbox and mandelbulb but they're not as great as the real mandelbrot set.
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Cyril Dugglekatch - Wed, 28 May 2014 11:45:08 EST ID:gQ1/L8ZJ No.14047 Ignore Report Quick Reply
>. And the degree to which they're naturally found in nature is grossly exaggerated by people lying for jesus, allah, brahma or whomever.
Not really. You're thinking of people spreading the 'golden ratio' nonsense, which isn't in nature that much. Many of the 'examples' of the golden ratio are just logarithmic spirals in general, and not the golden ratio.

Fractals appear in nature because they're developmentally easy to program, and they're fantastic at increasing surface area. That's why your lungs and vascular system are so fractally. Also, because of the loose definition of fractals, you can broadly apply the concept. for example, you can say a solar sytem is self-similar to a galaxy.

also this: http://en.wikipedia.org/wiki/Coastline_paradox
Cyril Dugglekatch - Wed, 28 May 2014 12:13:56 EST ID:gQ1/L8ZJ No.14048 Ignore Report Quick Reply
>for example, you can say a solar sytem is self-similar to a galaxy.
And I'm not saying the entire universe is a fractal, that's just an example of why fractals are so able to grab the imagination. If you try to extend that galaxy/solar system analogy further, it will fail.
Thomas Hembletane - Thu, 29 May 2014 11:43:54 EST ID:DMle3oF7 No.14050 Ignore Report Quick Reply
your apparent fractal likeness of the universe really means attractors, objects going back and forth around a midpoint the attractor, planets or an atom's brownian motion. an attractor doesn't have to be a point, it can be a set of points. strange attractors have fractal properties.
going out on a limb i suppose it has relevance down to quarks and quants (e.g. http://arxiv.org/abs/0806.3408, thx google, but i don't understand a word)

Best graphing calculator for nursing? by Hamilton Croshwitch - Tue, 20 May 2014 21:08:21 EST ID:X/gVZk08 No.14013 Ignore Report Reply Quick Reply
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Chem etc. Need to buy this like tonight I guess, and want a good one that will last through the next 5-6 years of school.
Nell Hottingforth - Tue, 20 May 2014 22:16:45 EST ID:SzH+rmP/ No.14014 Ignore Report Quick Reply
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Get a TI-84 Plus. I still use my TI-83 Plus from high school - they're pretty durable. So I don't have personal experience with the 84s, but they have great reviews.
Esther Hommerdodge - Wed, 21 May 2014 07:38:59 EST ID:uXKndL+s No.14016 Ignore Report Quick Reply
The TI-83 plus is all you need. I've had mine for about 5 years and it's still running strong.
That's only if you can find a new one though, don't bother buying a used one. If you can only find the TI-84 plus new, go with that.
Or you could go for the TI-89 ;) eye candy.
Esther Hommerdodge - Wed, 21 May 2014 07:42:53 EST ID:uXKndL+s No.14017 Ignore Report Quick Reply
I just found this, in the middle of installing so I can't recommend just yet...but it's free:
Nigger Grandstock - Thu, 22 May 2014 19:18:47 EST ID:8NxxczqH No.14023 Ignore Report Quick Reply
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Assuming its the same app/emu I use it works quite well
Samuel Bombleson - Fri, 23 May 2014 10:20:15 EST ID:4spVkkBQ No.14027 Ignore Report Quick Reply
TI-83/84 is great, but I suspect a nursing program would require a scientific calculator not a graphing calc

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