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Probability riddle

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2

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    #32
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    Say for example, I have a family with two female children. This is totally out of balance with nature. You on the other hand have a family with two sons, again totally out of balance with nautre. Yet put the two togeather and total harmony returns. This untimately does boil down to a macro/micro issue in my opinion.

    Yes, that's regression towards the mean. But there will be more families with a mix of boys and girls than with exclusively girls. Do you dispute this? That is what this thread is about.

    Your argument can be rephrased to say that having 2 girls is equally as likely to happen as having a boy and a girl. Do you think this is correct?


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    #33
    Fremen
    Registered Users Posts: 2,481 ✭✭✭Fremen


    Regardless of macro/micro issues, we're told that there is at least one girl.
    Could you help me out and list the possible combinations of brother/sister that this allows?


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    #34
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    Yes, that's regression towards the mean. But there will be more families with a mix of boys and girls than with exclusively girls. Do you dispute this? That is what this thread is about.

    Your argument can be rephrased to say that having 2 girls is equally as likely to happen as having a boy and a girl. Do you think this is correct?

    I do dispute your first point. My argument cannot be rephrased as you have said, I was merely pointing out the regression you have alluded to.


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    #35
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    Fremen wrote: »
    Regardless of macro/micro issues, we're told that there is at least one girl.
    Could you help me out and list the possible combinations of brother/sister that this allows?

    I already agreed with you on this:{BB,GG,GB,BG} The problem starts from here, where our opinions diverge. I cannot answer your question because it involves me accepting the very point that this debate is founded on


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    #36
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    I do dispute your first point. My argument cannot be rephrased as you have said, I was merely pointing out the regression you have alluded to.

    You said, with respect to 2 child families, that if you found out one child was a girl, that it is equally likely that the other child is a boy or a girl. Hence 'equally' likely. Correct??


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    #37
    Pherekydes
    Registered Users Posts: 16,124 ✭✭✭✭Pherekydes


    thetaxman wrote: »
    You are all incorrectly cancelling out 1/4 of the probability tree...

    The 1/4 of the probability sample space (not tree) is cancelled out when the lady in question tells you she has a daughter. Can you see why?

    What is your background, by the way?


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    #38
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    You said, with respect to 2 child families, that if you found out one child was a girl, that it is equally likely that the other child is a boy or a girl. Correct? Hence 'equally' likely. Are you flip-flopping?

    Did anyone see John Kerry about. I agree with your point, where is the flip-flop. It is equally likely because it is independent of the first child.


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    #39
    Pherekydes
    Registered Users Posts: 16,124 ✭✭✭✭Pherekydes


    thetaxman wrote: »
    I cannot answer your question because it involves me accepting the very point that this debate is founded on

    What? You can't accept that the woman has told you that she has a daughter?

    Or you can't accept that she has a daughter? :confused:


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    #40
    Pherekydes
    Registered Users Posts: 16,124 ✭✭✭✭Pherekydes


    Fremen wrote: »
    Yep, the maths PhD is wrong and you're right :rolleyes:
    This is beginning to look like a troll to me

    Looks like there is a first time for everything. :)


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    #41
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    I agree with your point, where is the flip-flop. It is equally likely because it is independent of the first child.

    Well, of course, you agree with your own point - I'm the one disputing it! :)

    Now if what you're saying above is true, then in families with two children, having 2 girls is equally as likely as having a boy and a girl. Do you agree with this?


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    #42
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    Slow coach wrote: »
    The 1/4 of the probability sample space (not tree) is cancelled out when the lady in question tells you she has a daughter. Can you see why?

    What is your background, by the way?

    I can see you reasoning, however it involves accepting an incorrect link.As for my background, lets just say I don't feel the need to use the Dr before my name, even though it would be justified based on my qualifications.


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    #43
    Fremen
    Registered Users Posts: 2,481 ✭✭✭Fremen


    once we're finished here, let's try explaining the monty hall problem...


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    #44
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    Fremen wrote: »
    once we're finished here, let's try explaining the monty hall problem...

    ...again! :)


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    #45
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    Slow coach wrote: »
    What? You can't accept that the woman has told you that she has a daughter?

    Or you can't accept that she has a daughter? :confused:

    Simple really, the link that the sex of the second child is affected by that of the first.


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    #46
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    Simple really, the link that the sex of the second child is affected by that of the first.

    Gah! Nobody is arguing that it is!

    This is not about the sex of one child influencing the sex of another. It's about distribution of sexes in groups being 0.5. Can't you see that??


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    #47
    Pherekydes
    Registered Users Posts: 16,124 ✭✭✭✭Pherekydes


    Fremen wrote: »
    once we're finished here, let's try explaining the monty hall problem...

    Maybe he's Professor Sir Roy Meadow. ;)


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    #48
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    Well, of course, you agree with your own point - I'm the one disputing it! :)

    Now if what you're saying above is true, then in families with two children, having 2 girls is equally as likely as having a boy and a girl. Do you agree with this?

    No I don't because you are connecting unrelated events.


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    #49
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    No I don't because you are connecting unrelated events.

    Ok, so if someone told you they had two children and one was a girl, and we know that in most two-children families with at least one girl, the other child is a boy...

    ...then it is more likely that the 2nd child is a boy than a girl!


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    #50
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops, you whole argument is based on this link, hence your cancellation of one of the four legs, that untimately results in your incorrect conclusion.


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    #51
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    Ok, so if someone told you they had two children and one was a girl, and we know that in most two-children families with at least one girl, the other child is a boy...

    ...then it is more likely that the 2nd child is a boy than a girl!

    This is not the case in most two children famalies. That is why I used the regression to mean example.


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    #52
    Fremen
    Registered Users Posts: 2,481 ✭✭✭Fremen


    http://en.wikipedia.org/wiki/Conditional_probability

    http://en.wikipedia.org/wiki/Boy_or_Girl

    Some light reading for you. I'm just glad you're not my taxman.


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    #53
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    2Scoops, you whole argument is based on this link, hence your cancellation of one of the four legs, that untimately results in your incorrect conclusion.

    You're the one that is conflating two entirely different issues, thetaxman. Namely, the independence of sex in births, and the even distribution of sex in groups.

    You are wrong. I suspect at this stage you are a troll. Sad.


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    #54
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    This is not the case in most two children famalies.

    So, you are saying that having 2 girls is equally as likely as having a boy and a girl, then? Care to check the census?


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    #55
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    So, you are saying that having 2 girls is equally as likely as having a boy and a girl, then? Care to check the census?

    Again, the census is macro not micro, I explained this. Debate my points, don't allude to a flawed website. Troll, give it a rest with your ad-hominem attacks.


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    #56
    Fremen
    Registered Users Posts: 2,481 ✭✭✭Fremen


    Maths isn't debatable, buddy


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    #57
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    There are many things which cannot be explained by science alone.


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    #58
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    Again, the census is macro not micro, I explained this. Debate my points, don't allude to a flawed website. Troll, give it a rest with your ad-hominem attacks.

    Macro and micro doesn't come into it. Probability is used to estimate the population values from samples. Yes, you get more variability in smaller samples but the fact remains that in two child families, having a boy and a girl is more common than 2 girls.

    Yes, you will get some with two girls and some with two boys. But for every family with 2 girls you will have two with a boy and girl, on average, with, of course, one boy/boy family to bring the average back in line with 0.5 probability of having a given sex.

    That is probability.

    Apologies for the ad hominem, but I simply can't believe you're not getting this.


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    #59
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    There are many things which cannot be explained by science alone.

    This isn't one of them. :)


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    #60
    thetaxman
    Closed Accounts Posts: 53 ✭✭thetaxman


    2Scoops wrote: »
    Macro and micro doesn't come into it. Probability is used to estimate the population values from samples. Yes, you get more variability in smaller samples but the fact remains that in two child families, having a boy and a girl is more common than 2 girls.

    Yes, you will get some with two girls and some with two boys. But for every family with 2 girls you will have two with a boy and girl, on average, with, of course, one boy/boy family to bring the average back in line with 0.5 probability of having a given sex.

    That is probability.

    Apologies for the ad hominem, but I simply can't believe you're not getting this.

    In my opinion it would roughly break down to 1/3 BB 1/3GG 1/3BG.


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    #61
    2Scoops
    Registered Users Posts: 1,845 ✭✭✭2Scoops


    thetaxman wrote: »
    In my opinion it would roughly break down to 1/3 BB 1/3GG 1/3BG.

    It doesn't though - it's 25% GG, 25% BB and 50% BG. Check any census you like.


This discussion has been closed.
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