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  • Monday evening puzzle
  • RealMan
    Free Member

    Mr Smith tells you he has 2 children. He introduces John, his son, to you. What is the probability he has two sons?

    Mr Jones tells you he has 2 children. He introduces John, his ELDER CHILD, to you. What is the probability he has two sons?

    Mr Johnson tells you he has 2 children. He introduces John, his son, to you, and tells you John was born on a Tuesday. What is the probability he has two sons?

    GrahamS
    Full Member

    I should know this… 😉

    Drac
    Full Member

    /has flashbacks.

    Stoner
    Free Member

    im hard pressed to think of why it’s not 50% for all three, but Im sure there’s a dastardly deviant reason why it’s not.

    (and Im assuming we’re not going into any odd days of the week gender distributions are we…)

    his eldest son

    that should be either “elder son”, implying two sons (100%) or he actually has 3+ sons (in which case it is also 100%)

    IanMunro
    Free Member

    1) 1/3
    2) 1/2
    3) 13/27 unless he’s standing on a conveyor belt.

    Robertwilkinson
    Free Member

    0%?

    tiggs121
    Free Member

    Smith and Johnson have one son each but Jones has two sons.

    RealMan
    Free Member

    Which of the sons is standing on the conveyor belt?

    Depends on the random distribution of conveyor belts in the local area relative to the sons, I’d assume. Impossible to say, I guess.

    (and Im assuming we’re not going into any odd days of the week gender distributions are we…)

    Not sure what you mean by that?

    j_me
    Free Member

    75%
    100%
    75%

    DavidB
    Free Member

    One quarter

    Stoner
    Free Member

    Not sure what you mean by that?

    Im wondering if there’s some freakishness of nature about the probability of boys or girls being born on various days of the week not being equal.

    Cougar
    Full Member

    Assuming the likelyhood of a boy or a girl is even,

    Smith – probability is 1 in 2, the presence of the first son makes no difference.

    Jones – “eldest son” implies two sons, otherwise it’d be “eldest child” – probability 1 in 1.

    Johnson – 1 in 2 again, what difference does the birthday make?

    RealMan
    Free Member

    Im wondering if there’s some freakishness of nature about the probability of boys or girls being born on various days of the week not being equal.

    Not that I know of, but in this question you can take the probability of being born on a certain day to be the same for each gender.

    Slightly reworded question 2, sorry for any confusion.

    McHamish
    Free Member

    Mr Jones definately has 2 sons…not sure about the other two.

    McHamish
    Free Member

    Just seen the update…haven’t got the foggiest for any of them.

    Stoner
    Free Member

    cougar and I think the same way. Probably both wrong then 🙂

    “eldest son” implies two sons

    superlative is used for 3+…so it implies three sons at least,
    Now edited by realman.

    IanMunro
    Free Member

    Slightly reworded question 2, sorry for any confusion.

    I wouldn’t worry, I’ve reworded my answer about four times so far 🙂

    Stoner
    Free Member

    “elder child”!

    what kind of cackhanded editing do you call that? The only one I was certain I knew the answer to…and now I dont! pah!

    j_me
    Free Member

    Smith – probability is 1 in 2, the presence of the first son makes no difference.

    It does make a difference.
    If he says he had 20 children what are the chances of him having 20 sons?
    He then introduces 19 sons (all called Dave)….Now what are the odds of having 20 sons?

    Its the old Goats and Gameshows.

    PeterPoddy
    Free Member

    Is it my imagination or is John doing the rounds a bit!

    It has to be 50/50 for all of them. The presence, age or recent birth of a son has no bearing at all on the sex of the other child

    Jones – “eldest son” implies two sons, otherwise it’d be “eldest child” – probability 1 in 1.

    Nope. Re-read it! 🙂

    PeterPoddy
    Free Member

    It does make a difference

    .

    No it does not. How can the sex of one child have ANY bearing on the sex of another?

    Gary_C
    Full Member

    I’m going to take a couple of Nurofen…..

    😕

    IanMunro
    Free Member

    You have to define ‘one child’ more carefully.
    ‘one of my children’ or ‘this one child, ere’

    j_me
    Free Member

    You aren’t convinced PeterPody ?

    Stoner
    Free Member

    I dont think this is the same as Monty Hall.

    Cougar
    Full Member

    cougar and I think the same way

    You have my sympathies.

    It does make a difference.
    If he says he had 20 children and introduced 19 sons all called Dave….what are the odds of having 20 sons.

    From a logic puzzle perspective, the odds are the same, 1 in 2.

    From a genetics point of view, the odds are somewhat higher I expect. I’m assuming it’s not that sort of a puzzle; if it is, I’m oot.

    Nope. Re-read it!

    You’ve changed it, you toe-rag.

    RealMan
    Free Member

    Ian, would you care to explain your working..? 😉

    IanMunro
    Free Member

    What, my real workings, or the workings I’d present if this was a presentation to a client? 🙂

    Cougar
    Full Member

    I wonder if one of the other two are grandparents, given the presence of Mr “John’s son” in the third one…

    Torminalis
    Free Member

    Assuming we are working on the basis that the male/female demographic split is 50/50 all of these have a 50% probability of having 2 boys.

    The day on which birth occurs has no bearing whatsoever so in each case we have 4 possibilities

    1) BB
    2) BG
    3) GB
    4) GG

    Question 1 omits possibility 4. 2 & 3 are effectively the same (in this case having no information on the order of birth) and are of equal probability which leaves us with 2 options, a boy and a girl or 2 boys. 2 options = 50%.
    Question 2 omits possibilities 2 & 4 which means it has to be 50%.
    Question 3 works out the same as question 1.

    What am I missing?

    RealMan
    Free Member

    I wonder if one of the other two are grandparents, given the presence of Mr “John’s son” in the third one…

    I like the thinking, shame its wrong. All separate questions, no one is related to anyone from a different question.

    What, my real workings, or the workings I’d present if this was a presentation to a client?

    I just want to know if you worked it out yourself or just googled it lol.

    brakes
    Free Member

    if you have two children, you will either have 2 sons, 2 daughters or one of each – 3 options
    therefore:
    1) we know John is a son so two options left so 1/2
    2) we don’t know any genders so 1/3
    3) we know one gender so are only left with 2 options, so 1/2

    (can I add that we can’t be sure that John is a boy)

    ph0010421
    Free Member

    2/1
    4/1
    2/1

    I was hoping for an opportunity to say ‘Burlington Berty’ here…

    RealMan
    Free Member

    2/1
    4/1
    2/1

    No, no, and no (and not just because 2/1=2, 4/1=4 etc).

    stratobiker
    Free Member

    I seem to remember reading somewhere that there are more boys born than girls. So it’s not a 50:50 ratio. But I don’t know what the figure is.

    RealMan
    Free Member

    I seem to remember reading somewhere that there are more boys born than girls. So it’s not a 50:50 ratio. But I don’t know what the figure is.

    You can assume that for any random child there is a 0.5 probability of it being a boy, and 0.5 for it being a girl.

    Torminalis
    Free Member

    So it’s not a 50:50 ratio. But I don’t know what the figure is.

    Men:Women 48:52 IIRC

    IanMunro
    Free Member

    1) BB
    2) BG
    3) GB
    4) GG

    Question 1 omits possibility 4. 2 & 3 are effectively the same (in this case having no information on the order of birth) and are of equal probability which leaves us with 2 options, a boy and a girl or 2 boys.

    Ah, 2 and 3 are not effectively the same, they are still two distinctly different configurations, so you have 3 options(1,2,3) and only 1 where the answer is BB so the odds are 1/3. Were you do say the eldest was a boy, then you have two options(1,2) (aasuming the eldest is listed first), so the odds are 1/2.

    The tuesday one makes my head hurt, so I’m not going into that 🙂

    Cougar
    Full Member

    I see where this is going.

    Looking at the first question: You have four possibilities,

    Daughter, daughter
    Daughter, son
    Son, daughter
    Son, son

    So when you know that one child is male, you rule out the first option. That leaves you with one out of three chances that both kids are boys.

    Robertwilkinson
    Free Member

    It’s all 0% surely as it’s about probability of lying and nothing to do with 49/51 gender split or age. Unless the questioner wants to tell us to assume the men are truthful?

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