Winamp & Shoutcast Forums Mathematical Logic [part 2]

2nd April 2003, 23:27   #361
xzxzzx
Forum King

Join Date: Aug 2002
Posts: 7,254
This is getting very interesting. However, your logic is flawed. GB/BG is not the same - well it is, but it's more likely than GG. Ok, let's look at how GG GB BG BB is constructed:

Samples = B/G+B/G
We have two possibilities, and two slots, so we have 4 possibilities (2^2):
```code:B + B/G
G + B/G
then
B + B
B + G
G + B
G + G```

If you had three children (2^3):
```code:B/G + B/G + B/G
-
B + B/G + B/G
G + B/G + B/G
-
B + B + B/G
B + G + B/G
G + B + B/G
G + G + B/G
-
B + B + B
B + B + G
B + G + B
B + G + G
G + B + B
G + B + G
G + G + B
G + G + G```

Or how about 21 children (assuming 20 of them are girls)
```code:GGGGGGGGGGGGGGGGGGGGG
BGGGGGGGGGGGGGGGGGGGG
GBGGGGGGGGGGGGGGGGGGG
GGBGGGGGGGGGGGGGGGGGG
GGGBGGGGGGGGGGGGGGGGG
GGGGBGGGGGGGGGGGGGGGG
GGGGGBGGGGGGGGGGGGGGG
GGGGGGBGGGGGGGGGGGGGG
GGGGGGGBGGGGGGGGGGGGG
GGGGGGGGBGGGGGGGGGGGG
GGGGGGGGGBGGGGGGGGGGG
GGGGGGGGGGBGGGGGGGGGG
GGGGGGGGGGGBGGGGGGGGG
GGGGGGGGGGGGBGGGGGGGG
GGGGGGGGGGGGGBGGGGGGG
GGGGGGGGGGGGGGBGGGGGG
GGGGGGGGGGGGGGGBGGGGG
GGGGGGGGGGGGGGGGBGGGG
GGGGGGGGGGGGGGGGGBGGG
GGGGGGGGGGGGGGGGGGBGG
GGGGGGGGGGGGGGGGGGGBG
GGGGGGGGGGGGGGGGGGGGB```

Quote:
 We KNOW for a 100% FACT that the first child is a girl.
Actually, we have no idea (well, there's a two in three chance) if the first child is a girl. We know that ONE of the children is a girl. If we knew the OLDER, or the YOUNGER one is a girl, then we know the other child has a 50% chance.

On another note, Ockham’s razor only really applies to competing theories when they come up with the same answer, or you cannot determine which answer is closer to truth: "Pluralitas non est ponenda sine neccesitate", indeed - note the last word.

Suppose that you have two competing theories which describe the same system, if these theories have different predictions than it is a relatively simple matter to find which one is better: one does experiments with the required sensitivity and determines which one gives the most accurate predictions.

Following that, here is an experiment. I assume that a coin probably has close enough to 50/50 landings to do this:

Flip two coins (or one coin twice), 20 times (or more, if you want to get more accurate), and record the results. Going through the pairs of flips, one at a time, have a friend ask you "is one of the pair of flips heads?" - if it is, mark down what the other flip is. So if the flips are HT (in whatever order), mark one for tails, and if it's HH, mark one for heads.

You will find, on average, that about you will have about 10 markings for Tails, and 5 for Heads, leaving the remaining 5 (which are not marked anywhere, as the answer was "no") with TT. Of course, your results will probably not be exactly this, but it will be close.

Rather than pointlessly argue, TRY IT, and see what you find, unless you think there's something wrong with the experiment.

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 3rd April 2003, 00:25 #362 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,161 IT IS FIFTY FUCKING FIFTY. My GOD cant you see that? You're making damn CHARTS to show weather it will be a boy or a girl. IT WILL BE ONE OF THEM, WITH EQUAL CHANCES OF IT BEING A BOY. I dont CARE what a fucking COIN TOSS will show, you have a GIRL already there, YOU CANNOT CHANGE THAT, THUS YOU ARENT "TOSSING" TWO COINS, YOU ARE TOSSING ONE, BECAUSE THE GIRL ISNT GOING TO MAGICALLY CHANGE. 50/50
3rd April 2003, 02:04   #363
has no CT
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Join Date: Sep 2000
Posts: 13,235
Quote:
 Originally posted by xzxzzx I don't understand how you can "stand by" two opposing answers, though.

I can stand by them both because I can see both sides of the argument

When you look at it mathematically, you answer is correct, i see that, but when you look at it from a biologist's stand-point, it is 50/50, no questions asked, so depending on the point of view, both answers can be considered correct

 3rd April 2003, 03:14 #364 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 The 67% answer is correct, both in actual practice, and mathematically. There are not two answers, there is one. The coin toss experiment is exactly what you would find in real life (assuming children were exactly 50/50, which they are not, but close enough). The point of view is irrelevant. If I had asked the question differently, the point of view would matter. However, it does not. It is not a biology problem. How can I convince you that it is 67%? Do I need to find some of the countless sites that agree with me? MY GOD, I EVEN POSTED AN EXPERIMENT FOR YOU. How the FUCK is it not the same as the riddle? Tell me that! What will it take? Maybe you can post an equivalent experiment, and I will do it? What you are forgetting is that we are not really solving what sex a child will be, but solving what the sex of two children will be. Because we do not know which of the two children is a girl, the 'problem' is not reduced to one child. Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 3rd April 2003, 03:21 #365 dlinkwit27 has no CT(Forum King)     Join Date: Sep 2000 Posts: 13,235 Ok, i guess for the particular question that you are asking, the 2/3 answer is correct. Happy?
 3rd April 2003, 03:36 #366 SSJ4 Gogitta Followed by Gnomes(Forum King)     Join Date: Dec 2000 Location: West Virginia Googolplex: 10^10¹°° FB:/SSJ4.DominusDeus DeviantArt: DominusDeus XboX GT: A Wild Meeseeks Playstation 4: DominusDeus Posts: 7,161 "Ok, here's one that should inspire some debate, and is more aligned You meet a long-lost HUMAN friend of yours. She brings along one of her two children, who is a girl. What is the chance that the other child is a boy?" "What you are forgetting is that we are not really solving what sex a child will be, but solving what the sex of two children will be. Because we do not know which of the two children is a girl, the 'problem' is not reduced to one child." yes you are. by asking "What is the chance that the other child is a boy?" you are asking us what chance it has of being of the male sex. One is a girl. that leaves a 50% chance the other is a boy. It does not matter WHICH one is a girl, it just matters that one of them IS a girl. Leaving it that we are trying to find the probibality of what sex the OTHER child is, which is 50/50. Now, if you would have said: "A woman has 2 children. What is the chance they will both be male?" Then i would agree that there would be a 25% chance on all male, 25% chance on all female, and 50% chance on a boy and a girl.
 3rd April 2003, 06:04 #367 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Delete me Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
3rd April 2003, 06:12   #368
xzxzzx
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Join Date: Aug 2002
Posts: 7,254
SSJ4_Gogitta, you are answering the wrong riddle. With that form of the riddle, depending on how you look at it, it is 50%, because which child, and the sex you find, is random. It is not, however (we now know the sex beforehand, and are now eliminating the chance of which sex is being picked), with this:
Quote:
 You come up to a couple, and find out that they have two children. You ask, "Is one of those children a girl?". They respond, "yes". What is the likelihood of the other child being a boy?
Quote:
 SSJ4_Gogitta Said:... i would agree that there would be a 25% chance on all male, 25% chance on all female, and 50% chance on a boy and a girl.
Ok, then, we eliminate the all male chance - that leaves 67% for m/f, and 33% for f/f. Right?

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 30th April 2003, 04:17 #369 xx1hotpunkxx Junior Member     Join Date: Apr 2003 Location: CA Posts: 29 Good point...very good point....?????
 30th April 2003, 06:37 #370 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 If you still don't agree, perhaps these sites can convince you: http://www.greylabyrinth.com/Puzzles/puzzle054.htm http://mathforum.org/dr.math/faq/faq.boy.girl.html Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 30th April 2003, 07:42 #371 Winsane Moderator Alumni     Join Date: Jun 2000 Location: U.S. (eastern time zone) Posts: 2,598 Wow. Good thread, though frustrating to read towards the end. The answer to the boy/girl question just depends on how you phrase the question. Ignoring biological factors, family planning, hermaphrodites, and such: You ask a mother with two kids: "Is one of your children a girl?" She says yes. P(2nd child is a boy) = almost 1. If both were girls, most people would respond something like "No, both of them are girls." They'll infer that you meant logical XOR rather than logical OR. You ask a mother with two kids: "Is at least one of your children a girl?" She says yes. P(2nd child is a boy) = 2/3. Xzxzzx explained this case over and over again, but never really phrased the setup correctly. You meet a mother with two kids. One of them is with her, and is a girl. Or: You meet a mother with two kids. You find out that the older one is a girl. Or: Most of the other ways of putting the problem which I've forgotten already that were posted in this thread. P(2nd child is a boy) = 1/2. Rumata clearly understands this, and is correct. Anyone care to argue with that? And another thing that always goes all the way through a door (when present) is a peep-hole. Anyone care for a poker probability question that'll take way too long to solve correctly? (Warning: I've got the correct answer, but might be too lazy or absent to explain it.)
 30th April 2003, 13:31 #372 james Forum PFY(Major Dude)     Join Date: Jan 2001 Location: WR3 or NG7 Posts: 6.2+3i Posts: 1,698 Everyone knows that the third word in the english language ending in -gry is nugry.... :P <3 ESR He uses statistics like a drunk uses lamp-posts: for support, not illumination.
30th April 2003, 16:07   #373
xzxzzx
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Join Date: Aug 2002
Posts: 7,254
Quote:
 Originally posted by Winsane You ask a mother with two kids: "Is one of your children a girl?" She says yes. P(2nd child is a boy) = almost 1. If both were girls, most people would respond something like "No, both of them are girls." They'll infer that you meant logical XOR rather than logical OR.
Uh, ok, then the chance is even further from 50%, it is 100% - there is no "chance" at all.

Quote:
 Originally posted by Winsane You ask a mother with two kids: "Is at least one of your children a girl?" She says yes. P(2nd child is a boy) = 2/3. Xzxzzx explained this case over and over again, but never really phrased the setup correctly.
I think everyone clearly understood the question was "at least one". No one argued it was 100%.

Quote:
 Originally posted by Winsane You meet a mother with two kids. One of them is with her, and is a girl. Or: You meet a mother with two kids. You find out that the older one is a girl. Or: Most of the other ways of putting the problem which I've forgotten already that were posted in this thread. P(2nd child is a boy) = 1/2. Rumata clearly understands this, and is correct.
Obviously. You have to predetermine the sex that you want to ask about, and must do so from the selection of the two, not just the child that happens to be brought along.

Oh, and as for the poker probability question, bring it on!

Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything.
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 30th April 2003, 21:03 #374 cyana total eclipsed(Major Dude)     Join Date: Apr 2001 Posts: 1,488 The answer of course is 67% for a boy - it's called indirect (or dependend) probability. There was a similar riddle by Maria vos Savant (the person with the highest IQ ever measured) some years ago, that uses Bertram's selection paradoxon to get you into the strange world of dependend probability, that sometimes seems to speak against our 'natural' sense of logic ... the Southern Pinwheel Project A conversation with our universe googlism note of the week: cyana is going to be the last thing you ever see
 30th April 2003, 21:44 #375 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 So post it! Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 30th April 2003, 22:12 #376 cyana total eclipsed(Major Dude)     Join Date: Apr 2001 Posts: 1,488 the Southern Pinwheel Project A conversation with our universe googlism note of the week: cyana is going to be the last thing you ever see
 22nd September 2003, 20:22 #377 Raz Forum King     Join Date: Dec 2002 Location: Manchester Posts: 6,470 bump
 22nd September 2003, 21:39 #378 xzxzzx Forum King     Join Date: Aug 2002 Posts: 7,254 Wow, I remember this thread... And damn it, it's 2/3! Just TRY IT! Freedom of speech is the basic freedom of humanity. When you've lost that, you've lost everything. 1\/\/4y 34|<\$p4y 1gp4y 33714y, 0d4y 0uy4y? | Roses are #FF0000; Violets are #0000FF; chown -R \${YOU} ~/base The DMCA. It really is that bad. : Count for your life.
 Winamp & Shoutcast Forums Mathematical Logic [part 2]

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