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Geek Culture / The Girl and Boy Paradox

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Insert Name Here
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Posted: 26th Nov 2007 22:00
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This is an interesting paradoxy thing. Basically, you are given two questions, that at first glance seem identical, but actually there is a differetiation of probability if looked at closely. The two questions being:

A random two-child family whose older child is a boy is chosen. What is the probability that the younger child is a girl?

A random two-child family with at least one boy is chosen. What is the probability that it has a girl?

Let us assume there is an equal chance of a child being a boy or a girl. In question B you have the three possible choices, ass GG is impossible, there must be at least one boy: [BB,BG,GB]
This gives us a 66% chance of a girl.
But in Question A you only have two possible choices, because GG and GB are impossible, the older child is always a boy. So: [BB,BG]
This gives us a 50% chance of a girl.
Slightly interesting.


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Peter H
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Posted: 26th Nov 2007 22:08
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well... yeah.

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David R
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Posted: 26th Nov 2007 22:25
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Don't think it could really be called a paradox though


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Insert Name Here
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Posted: 26th Nov 2007 22:30
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True, it's kinda like a retrospective mishap.


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NeX the Fairly Fast Ferret
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Posted: 26th Nov 2007 22:37 Edited at: 26th Nov 2007 22:38
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Let us assume there is an equal chance of a child being a boy or a girl. In question B you have the three possible choices, ass GG is impossible, there must be at least one boy: [BB,BG,GB]
This gives us a 66% chance of a girl.

Wrong. You have BB twice, as there are two arrangements of BB. There is always a 50% chance, and if it was truly random, nothing could change that.


Since the other one was scaring you guys so much...
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Peter H
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Posted: 26th Nov 2007 22:47 Edited at: 27th Nov 2007 13:31
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[edit] nevermind

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NeX the Fairly Fast Ferret
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Posted: 26th Nov 2007 22:48
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No, there is no GG as at least one family member is a B.


Since the other one was scaring you guys so much...
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Peter H
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Posted: 26th Nov 2007 22:51
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ah, true, my fault for not reading closely enough.. i gotta go somewhere so i was rushing

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NeX the Fairly Fast Ferret
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Posted: 26th Nov 2007 22:52
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Random chances like this should never deviate from 50%. Right? Not taking into account genetic biases, etc.


Since the other one was scaring you guys so much...
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demons breath
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Posted: 26th Nov 2007 23:08
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It is 50%... it doesn't matter which order the children were born in. Well it might to them, but for our purposes not so much.

If the question was "what is the chance that the older child is a girl" or something along those lines for b then the order would be relevant. But it's not. So it isn't. So there you have it.

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The crazy
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Posted: 26th Nov 2007 23:40
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You all have it wrong.... You are not factoring in the transgender individuals! What about Richard Simmons or Rosie O'donnell?? How dare you overlook such an important factor in the equation.

For shame...

But more seriously, what about Conjoined twins and one is a boy, one is a girl?

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David R
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Posted: 27th Nov 2007 00:03 Edited at: 27th Nov 2007 00:04
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That question kind of leads to "How do you define what is a human being". Logically I'd say a conjoined twin is two separate people (so, a boy and a girl in your above example), but it could depend entirely on what organs/body parts are shared between them


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Grandma
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Posted: 27th Nov 2007 00:05
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Quote: "a conjoined twin is two separate people"


I find that highly ironic.

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David R
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Posted: 27th Nov 2007 00:10 Edited at: 27th Nov 2007 00:11
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Quote: "I find that highly ironic."


Well seeing as though twin implies two, a conjoined twin is merely two things connected together. Just because they form/are counted as one entity doesn't make them any less two separate objects (which happen to be connected). But it depends how they are connected together, of course.


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Grandma
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Posted: 27th Nov 2007 00:16
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Ofcourse, I was just trying to point out something that made me smile a bit.

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Venge
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Posted: 27th Nov 2007 03:40
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Separate conjoined twins....maybe an oxymoron
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Chily Dog
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Posted: 27th Nov 2007 08:08
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Ewww...you got genetics all over my shirt
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Hobgoblin Lord
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Posted: 27th Nov 2007 10:10
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Quote: "A random two-child family with at least one boy is chosen. What is the probability that it has a girl?"


assuming no one in the family is dead, and the parents are the childrens actual parents then the chance is 100%

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Cash Curtis II
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Posted: 27th Nov 2007 11:39
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Quote: "Let us assume there is an equal chance of a child being a boy or a girl. In question B you have the three possible choices, ass GG is impossible, there must be at least one boy: [BB,BG,GB]
This gives us a 66% chance of a girl."



There are not three possible choices, there are only two - boy or girl. Child #2 can only be either a boy or girl and has an equal chance of being either. Using the pairs as choices is misleading because the chances of achieving a certain pair is not 50%. The logical fallacy is that the second choice is contingent upon the first, but it is not.

Who showed you this? They should slap themselves for trying and failing to be clever.


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Libervurto
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Posted: 27th Nov 2007 17:54 Edited at: 27th Nov 2007 17:56
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I agree with Cash
if a two-child family already has a son, their second child is either a boy or girl (50%)
If the first child was a girl the second child has to be a boy or the family is invalid, so it's a 50% chance again but this time looking for a boy and not a girl.

and like nex said: if you are going to count every possible combination of children with at least one boy you'd get
BB, BB, BG, GB
which is still 50%

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aluseus GOD
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Posted: 27th Nov 2007 18:54
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This reminds me of the monty hall paradox. I'll post it later, because I tried posting it, but it didn't work, and I couldn't recover the post ><

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demons breath
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Posted: 27th Nov 2007 18:56 Edited at: 27th Nov 2007 19:03
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oh yeah... if that's what I think it is, then it's a pile of poo. My teacher tried to explain it to me... It's rubbish.


EDIT: AHHHH WAIT! I get it now. Good old wikipedia. It's not really a paradox either though, is it?

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Peter H
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Posted: 27th Nov 2007 19:29
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yeah, we call that and the "birthday paradox" misnomers.

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Posted: 27th Nov 2007 20:13
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Quote: "Wrong. You have BB twice, as there are two arrangements of BB. There is always a 50% chance, and if it was truly random, nothing could change that."

Well done, you were the first person to spot that.
Quote: "Who showed you this? They should slap themselves for trying and failing to be clever."

OK, I'll just go and slap Wikipedia.

No seriously, I was fully aware of this problem, having read the entire wikipedia article about it (Yes I'm a cheat). I wanted to see who would be clever enough to spot the two BB problem.
So well done all of you.


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NeX the Fairly Fast Ferret
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Posted: 27th Nov 2007 20:18
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w00t.


Since the other one was scaring you guys so much...
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Posted: 27th Nov 2007 20:41
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Hehehe. Indeed.


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Pus In Boots
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Posted: 27th Nov 2007 21:20
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Quote: "Random chances like this should never deviate from 50%. Right? Not taking into account genetic biases, etc."


It would be 50%, genetics included. Each parent has a gene for boy or girl. Their dominant genes would be diferent, because that's their gender. The recessive genes would be the other gender, so it's BG and GB. 50-50, eh?

See? I can be clever too.

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Posted: 27th Nov 2007 21:36
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Only occasionally.


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Pus In Boots
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Posted: 27th Nov 2007 21:39
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That hurt

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demons breath
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Posted: 27th Nov 2007 22:16
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@Pus: That's not how it works is it?

I thought it was XX or XY - you automatically get a X chromosome from your dear mother, and if your father blesses you with a Y chromosome then you become male, whereas if he sees fit to give you an X chromosome then you become female.

Mind you, I never paid much attention in science - much preferred to conduct my own experiments like "I wonder what happens if I snort the product of this experiment" or "I wonder what the difference between the taste of acid and alkalis is"

I got banned from doing experiments or coming near chemicals.

Probably for my own good as well.

I would SERISOULY advise no-one tries any of that.

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Venge
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Posted: 27th Nov 2007 23:50
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Quote: "I wonder what the difference between the taste of acid and alkalis is"


A couple of people in my chemistry class were making bets as to how much hydrochloric acid they could drink and still live, until the teacher told them it would burn a hole in their stomach.
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demons breath
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Posted: 27th Nov 2007 23:53
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haha well done.

Worst I did was snorting some black powder stuff... think it was Copper Oxide or something... that hurt like hell for about 6 hours all up my nose and along the right side of my brain but then it calmed down a bit. Not doing that again...

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Venge
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Posted: 28th Nov 2007 00:04 Edited at: 28th Nov 2007 00:04
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One day we were working with chemicals to see if they would react with different metals...I think I inhaled some vapors or something, my throat burned for the next few days. It might have been putting the piece of magnesium in hydrochloric acid...That thing was gone within minutes.
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demons breath
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Posted: 28th Nov 2007 00:07
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Oh yeah magnesium was always great fun to play with.

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aluseus GOD
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Posted: 28th Nov 2007 02:18
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Hydrochloric acid burns holes in your stomach? Gee, It's a good thing I decided not to the other day.

alus.portbb.com go there.
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Jeff032
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Posted: 28th Nov 2007 05:58
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Isn't magnesium that stuff that burns really really brightly?

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NeX the Fairly Fast Ferret
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Posted: 28th Nov 2007 18:43
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Isn't the acid in your stomach hydrochloric? Magnesium is very reactive indeed, and burns so brightly it can cause blindness after prolonged exposure.


Since the other one was scaring you guys so much...
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GatorHex
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Posted: 28th Nov 2007 18:58 Edited at: 28th Nov 2007 19:09
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Demons Breath wrote:
Quote: "I wonder what the difference between the taste of acid and alkalis is"


Safer would taste vinigar(acid), then taste baking soda(alka).

Then put the baking soda in your vinigar pot an shake

A paradox is unsolvable like if you travel back in time and kill you grandfather are you born? If you're not born how can you go back and kill him

If you want to disintigrate a person acid wont do it fully because of dilution with your body fats. Aparantly biological washing powder is much better as it will eat everything

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Benjamin
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Posted: 28th Nov 2007 19:03
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Quote: "Safer would taste vinigar(acid), then taste baking soda(alka)."

Who is Safer and why would he taste both these things?

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GatorHex
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Posted: 28th Nov 2007 19:12 Edited at: 28th Nov 2007 19:21
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Quote: "Who is Safer and why would he taste both these things?"


Demons Breath, coz curiosity killed the cat? (Is that an Idiom or a Proverb?)

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Libervurto
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Posted: 28th Nov 2007 19:54
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how are you all still alive?
That Monty Hall was pretty clever actually, this gender this is a load of bull though

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David R
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Posted: 28th Nov 2007 20:44
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Quote: "how much hydrochloric acid they could drink and still live, until the teacher told them it would burn a hole in their stomach."


Yeah, drinking HCl which is already present in your stomach would clearly burn a hole through it...


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Benjamin
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Posted: 28th Nov 2007 20:45
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Quote: "Yeah, drinking HCl which is already present in your stomach would clearly burn a hole through it... "

Depends on the concentration.

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Libervurto
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Posted: 28th Nov 2007 20:56 Edited at: 28th Nov 2007 21:00
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When you throw up and it burns that's HCl
Drinking a bottle of the stuff would give you more than a sore throat
I don't think it would make it to your stomach before you were leaking like a tin can with bullet holes in it (not externally )

Even stronger than that is sulphuric acid, that stuff can burn through floors!

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Posted: 28th Nov 2007 21:30
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I beleive the worst thing I have ever seen anyone in my science class do is when I knocked a pot full of hihgly concentrated acid down myslef.
The buuuurns!


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Libervurto
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Posted: 28th Nov 2007 22:09
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That's quite bad that the worst thing you've ever seen someone do was you doing it

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Venge
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Posted: 28th Nov 2007 22:56 Edited at: 28th Nov 2007 22:57
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Quote: "Yeah, drinking HCl which is already present in your stomach would clearly burn a hole through it... "


Let me rephrase that. The hydrochloric acid would burn holes in your esophagus, causing internal bleeding and possibly leaking acid into your chest cavity to burn away at all your other organs. Is that better? Or should I tell you that pure hydrochloric acid is much stronger than the stuff in your stomach, and would have no problem eating through the lining that protects us from the more diluted stomach acid.

Still don't believe me? Go drink a beaker full then.
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demons breath
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Posted: 29th Nov 2007 04:37
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Quote: "Safer would taste vinigar(acid), then taste baking soda(alka).

Then put the baking soda in your vinigar pot an shake"


@Gatorhex: but where's the fun in that?

At least it was mostly better than my tech (DT) classes...

I tended to do what people dared me to when i was in about year 10 and 11

"Let me smack your hand with this hammer"

"Can I drill through your nail?" <-ok that wasn't too bad but i needed to get rid of the pressure 'cos it turned black within about 15 seconds of the above hammer attack

"If I put this bit of hot wood on your hand, how long can you leave it before you have to take it away" (he took it away - felt kinda proud till I noticed it left a scar which hasn't gone away years later)

"Put your nose on the band facer" <- for those of you who don't know, it's like a machine with really hard, abrasive sand paper spinning round really fast. Not clever. Plus some little particles come off giving a good salt-in-the-wound effect.


Yeah when I was younger I tended to do stuff like that to get attention... glad I grew out of that... Wasn't turning out too well...

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The worst thing I have ever heard of someone doing in school was when my friend got hit over the head with a rolling pin and got extensive brain damage...


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GatorHex
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Posted: 29th Nov 2007 11:14 Edited at: 29th Nov 2007 11:15
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Quote: "@Gatorhex: but where's the fun in that?"


well obviously you not put "vinegar and baking soda" into youtube

I've seen people do the same with stronger acids but I wouldn't recommend something as stupid as that coz u just gona get hurt or in trouble with the law

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