Kamala Trump
Verified User
wrong.
Quick Logic Problem
- Thread starter KingCondanomation
- Start date
Kamala Trump
Verified User
There is a 1 in 2 chance of woman with one boy having another boy. This is WITH REPLACEMENT, to use statistics parlance.
The family isn't the variable. The only variable is the child of unknown sex. You are again applying bad math. I keep saying it, but it applies strongly here, it is the "missing dollar" scenario.Damo, this is nuts, the example is well-known in probability theory, read it:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Bayesian approach
Consider the sample space of 2-child families.
Let X be the event that the family has one boy and one girl.
Let Y be the event that the family has at least one boy.
Then:
Or, the set {GB, BG, BB}, in which two out of the three possibilities includes a girl.
Therefore the probability is 2/3.
Ok, done, over. There is a 2 in 3 chance of a woman with one boy having a girl and thus a 1 in 3 chance of having 2 boys.
KingCondanomation
New member
1. What determines what is logically correct is the probability, NOT statistics.
2. The only statistics actually used (after the fact) back up what the probability said - that women who have 1 male child have a 1 in 3 chance of also having another boy.
I strongly suspect you guys are mired in this mode of thinking the woman is pregnant with her 2nd child after having a boy and we need to guess what the next child will be. Of course that would be 50/50.
Kamala Trump
Verified User
I meant probability.
So this is really about some quirk in biology then. Would this answer be the same if we were using actual coin tosses?
KingCondanomation
New member
Wrong. The MISSING variable is the child of unknown sex, the other variables are of course needed and included in the formula to determine the missing variable.
You have a degree in math, I have one in computer science. You reach a solution by trying to theorize in your head how it would work, it's my job to actually do the implementation that leads to a solution.
The formula is there, are you saying it's wrong, if so which part is wrong? Be specific.
They are not variable.
1 child boy is the given.
Given - Girl
Given - Boy
Girl - Given
Boy - Given
Are the only possibilities.
It is figured in exactly the same way as "two people flipping coins" that I stated earlier.
KingCondanomation
New member
Do 1000 coin tosses of 2 coins at a time. Eliminate all those tosses where BOTH coins show as heads, leaving you with only those tosses where there are either (your goal here is to see the chances of getting both as tails):
1. heads on first coin, tails on second coin
2. tails on first coin, heads on second coin
3. tails on first coin, tails on second coin
Damo is saying that if I name those coins, I would somehow be able to reverse the last case (to get a 1 in 2 shot of having both as tails, but somehow I am NOT allowed to reverse the first 2 cases).
It's a common mistake and is talked about in the link that I gave. You would find that each case would occur about 1 out of 3 times, including the case with both coins showing as tails.
KingCondanomation
New member
Damo, it's not a silly link, it IS the problem and it's well known enough to appear in Wikipedia. Are you saying it is wrong?
When figuring probability on the next coin flip, the previous coin flips are always irrelevant, it simply does not matter how many times you flip a coin, it is a 50% probability of landing heads the next time. (or when figuring the 'unknown' previous coin flip the known figure is not relevant.)
I suppose we'll find out, if I keep going. I need to learn to just let it go.
Kamala Trump
Verified User
Thorn
Member
I do that when I realize that it's hopeless.
KingCondanomation
New member
And as already stated, those answers don't come up in the same frequencies. If you don't believe me then look at the results from her survey.
Let's say I am going to have 2 kids and am guaranteed that at least one will be a boy.
So I say I want to name my first child John and 2nd child James or I would name my first child John and 2nd child Jill or I would name my first child Jill and 2nd child John.
Still 1 in 3. What you are arguing is that I could name my first boy James and 2nd child John, then I would say Ok, why can't I then name my first child James and 2nd child Jill OR first child Jill and 2nd child James.
You can't include that extra case without the other 2 and there is no way to escape from it being a 1 in 3 chance of having 2 boys.
If both coins are variable (both unknown) you have three possibilities.
heads-tails
heads-heads
tails-tails
When one is given, you are figuring the probability of only one coin and it becomes 50%.
Given - Heads
Given - Tails
The problem Dano is having is understanding the principal of "The Given" and misapplying the variable therefore.
John could not be "James" too. The given remains the given regardless of the "birth order".
heads-tails
heads-heads
tails-tails
When one is given, you are figuring the probability of only one coin and it becomes 50%.
Given - Heads
Given - Tails
The problem Dano is having is understanding the principal of "The Given" and misapplying the variable therefore.
John could not be "James" too. The given remains the given regardless of the "birth order".
KingCondanomation
New member
MottleyDude got it, the problem is right here and explained, they even explain the exact mistake Damo made (and possibly you).
Please read it and see for yourself:
http://en.wikipedia.org/wiki/Boy_or_Girl_paradox
Kamala Trump
Verified User
King. Are we NOT assuming that when we flip a coin we have a 1 in 2 chance of getting a tail?
KingCondanomation
New member
Damo, the problem is at the beginning, you do not have 3 possibilities, you have 4 possibilities:
heads-tails
heads-heads
tails-tails
tails-heads
There is only ONE way to get heads-heads, you flip the first coin and get heads and then you flip the 2nd coin and get heads. That's it, no other way.
To get a combination of heads and tails, you can either:
Flip the first coin and get heads and flip the 2nd and get tails
OR
Flip the first coin and get tails and flip the 2nd and get heads
Tell me you can agree with that. All the evidence produced backs what I said up.