This week the puzzle comes via Mike Heap and the wonderful ASKE organisation.
A few months ago I ran a classic puzzle along the lines of …..‘Jane has two children. One is a daughter. What’s the probability that her other child is also a daughter?’
Now, here is a second part to the puzzle…
‘Jane has two children. One is a daughter named Emma. What’s the probability that Jane has two daughters?’
As ever, please do NOT post your solutions, but do feel free to say whether you think you have solved it and how long it took. Answer on Monday.
P.S. Just to remind you that if you are into magic, I have 5 free online passes to give away to the Essential Magic Convention. To stand a chance of winning a pass, just email me with Harry Houdini’s real name. On Monday I will randomly choose 5 lucky winners and email them the code that they need to watch the event.
Richard Wiseman 
I just could not see any difference in the previous puzzle and this one presented now as ‘second part’. In probability logic, how does the name of first daughter should matter?
It matters a lot!
Easy, unless I missed something…? A few seconds to think through it. I’m assuming the question is meant to imply “What’s the probability that *Jane* has two daughters?” and not “What’s the probability that *Emma* has two daughters?”
Strictly speaking, “she” refers to the last person mentioned, and that is Emma. So the question is indeed the probability that Emma has two daughters.
Probably the answer has something to do with letting Jane live or die (as in previous puzzles) 😉
@Richard, change the “She” for “Jane”! Your readers are very picky. 🙂
As a linguist who is looking at how pronouns (and other referring expressions) function, I’m not sure that you can say that ‘she’ necessarily refers to the last person mentioned.
Consider the following utterance:
‘Jane hugged Mary, and then she hugged Sue’
When ‘she’ is unstressed, most people interpreted it as referring to ‘Jane’ and not to ‘Mary’. This changes when you stress ‘She’.
All sorts of things contribute to how we interpret pronouns – the topic of the sentence, the rest of the discourse context and so on.
Personally, I think it’s a very interesting area, but then I have just written a PhD thesis on it….
You go, Kate! I love when other people bust out some real linguistic knowledge, not just that “You said “Brian and me went to the concert’ but you should have said ‘Brian and I went to the concert’! How do you expect anybody to understand what you’re saying if you don’t use proper English? I mean, I had no idea what you were saying until I realized you meant ‘Brian and I’!” prescriptivist bullshit. 🙂
Very nice puzzle, with a very non-intuitive answer. Its only weakness is certain assumptions we have to make to get a precise answer. I came across one very alike, very recently… Monday, I’ll explain what Tuesday means.
Hey Pirate Joao Pedro you seem to love these type puzzles but this here pirate don’t like probabilities……’cause the odds always seem to be against me! Why can’t we just go to Jane’s house and ask her? No wait she would probably say if I can’t tell a census worker why would you think Richard would let me tell you? Hmm let me flip the hour glass and have a sip of watery wine from that bucket and maybe try counting windows as long as the mad monkey will stop stalking me demanding banana juice….. what was the question?
The odds are always against us, and that’s good so. It is better to dream with gold than to have it.
classic
The Drunkard’s Walk – How Randomness Rules Our Lives
Two answers based on which assumption is made (as Joao Pedro Afonso says, Tuesday is important) – although both answers are different, one is imprecise and only infinitesimally different. Having read about this puzzle form in detail after part 1, this didn’t take any time.
Well it depends if the children have the same dad, also on Janes diet and both parents upbringing and what they have been exposed to in their lives- I could go on, but in reality I don’t know the answer so will have to wait until Monday!
Have a good weekend. 🙂
Ah correction…..the gender of a human child is totally up to the man…..the female only has to carry it, give birth to it and then deal with it until the day the “mom” draws her last breath….so let’s make sure that the one thing the male is 100% responsible for get to take full credit!
I think Marion is referring to some ideas where the food influences the chemical environment where the spermatozoa had to swim or the fertilized egg had to fix. If the motility or the grow factors is somehow dependent on the transported genes, different environments might filter this or that gender in the statistical sense. In other words, even if both genders start with equal probabilities when they came out of the male, they might be not so, in the moment we want to know what is going to born. And that is indeed, almost 100% mother (less indirect factors)
It also depends on when Jane ovulated relative to when copulation occured. The Ys swim faster but the Xs live longer. That explains our girl after 3 boys. (Never think “Ok , we’re probably safe now”!).
yeah, yeah but still it comes down to the male and his ratio of HIS Xs and Ys…..cause it really won’t mount to a hill of beans if most of whats there is more or less or next to none of one or the other no matter how fast they swim or how pleasant the surrounding environment might be…..lol… I took a nap and feel better now…. :}
Lol. Wayhey, Lilabyrd spoke to me. (over-exuberance caused by 12 hours working quickly followed by 2 glasses of wine). Have enjoyed your comments here over the last few weeks – sometimes I find the tangents more interesting than the puzzles (shhh, don’t tell Richard).
LOL Wayhey Rusty glad it took so little for you to have fun! Yes the tangents are fun too…. and any time you don’t want Richard to know just do what I do….tell him not to look or take my lap top into the closet and if you are using a PC then just turn the lights off and type quietly……that should do it!
A male deposits a quantity of semen, containing both ‘male’ and ‘female’ sperm (I know, but that will do for now).
The idea that the male is solely responsible for which of these ultimately fertilises the egg is preposterous.
@LordManley are you in the medical profession? Ever work in the OB/GYN field….I have and even delivered babies…..and natural as in NOT messed with by out side medical assistant …..the male alone can decide the gender of said baby. What is preposterous is how many times the female gets blamed because no male child is conceived and she must do something to make a male child and she isn’t the one that can do that only the male can.
And once the ovum leaves the ovary it enters the fallopian tube and travels to the outer third of the fallopian tube {ampulla} and STAYS there to await fertilization and is viable only for 18-24 hours if not fertilized it is absorbed into the body. Timing may have a lot to do with fertilization but what it comes down to gender it is the male and his ratio of X and Y and motility of said sperm. There are many so called ways to try and make the chances more one way or the other but are not proven by any scientific process in natural conception. Now conception that is medically assisted is a whole other critter.
I predict this will generate more comments than any other of recent times!
Joao Pedro Afonso:> I saw the Tuesday one too recently and after reading all the comments decided to give up trying to decide who was right!
I hope my reference to Tuesday didn’t spoiled this puzzle to you. Are you saying that it is a very polemic puzzle?
One minute. I didn’t do any checking on Wikipedia, so I hope I employed the right mathematics!
Currently reading ‘The Drunkard’s Walk’ by Leonard Mlodinow, where this very problem/question is dealt with. Great example of Bayes’ theorem.
Answered in <1 second and have been wracking by brains for 5 minutes trying to convince myself otherwise. Can't find any other answer than the obvious one, and no difference whatsoever from the first half of the puzzle.
Yeah, same here.
Well I worked out the probability of Jane having two daughters quite quickly – two minutes. However, I’m a bit stumped with the Emma part …. Guess I’ll have to wait until Monday 😦
COME HERE OFTEN?
@lilabyrd
Nah, first time. Saw the post on BBQ on your blog, really funny 😀
Thanks I sometimes ruffle a few feathers of some of my fellow environmentalist with my twisted humor as I am not a veggie or vegan…..I believe in healthy balanced moderation and the world can be a good place and even get better… and I like my sick humor…..and welcome to our fun on Friday…..and the weekend too! We really don’t post answers either right or wrong until Monday when Richard will post HIS answer and then we pick it a part until this time next week…lol….Over the week end we just drop hints say if we got it or not and so on…..enjoy!
Ahh sorry I just quickly read the question, not the rule mentioned in the post. I can’t see a delete button to remove my comment. Needless to say, I won’t mind at all if the moderator deletes this post – Richard if you are reading this please go ahead.
I knew intuitively what the answer would be like, and it took me about 15 minutes to calculate the exact probability with the assumptions I have outlined.
@lilabyrd
PS. Was it you who put up that signboard? Hahahha
aha.. Drunkyards Walk – funny to learn to calculate this
How about “one of her children is older than the other one”. That’ll really get the arguments going.
wait you know full well that they {her children} were born at the same time to the nanosecond! Even if it was at two separate locations!
Arnab Bose that is OK everyone makes mistakes but sometimes folks that come here all the time just can’t seem to help them self….those folks piss people off…lol….but it is just a Friday Puzzle….but don’t tell Richard that wouldn’t want to hurt his feelings….lol….don’t read this Richard OK? And the sign….wish I could take credit but no not me THIS TIME….hehehe…
May I suppose then that whatever Arnab Bose wrote, is already deleted? I’m unable to see whatever he/she made that he/she need to apologize for.
what might or might not be the answer…..hehe…I just came back to look for a few but now must really go and get some sleep… it’s just after 12 noon here and I have as to yet gone to sleep so been up all night and half the day! So to sleep I go and will come back later….have a good day…Joao Pedro…and we can discuss the gender issue a few posts up…lol……
I actually know the woman in question; I think she lives in Austen as of last reckoning. 🙂
If this is simple probability, it only took me about a minute. I’m interested…
So… am I missing something, or is the answer blatantly obvious? I can’t think of any reason why it should be anything other than… well… you know what.
Is it a double meaning on ‘one’?
One of the two children vs child number One, the first born
child?
If not I can’t see any difference to the ‘traditional 2 child problem’
Ach! I know now!
Supposing you have read both
http://blogs.ft.com/undercover/2010/07/the-boy-problem/
and
http://news.bbc.co.uk/2/hi/programmes/more_or_less/8735812.stm
you should be able to know too!
It’s not like in “Tuesday”, because it’s not from a limited set of possibilites — 7 days versus an “infinity” (sort of) of names.
Also, keep in mind that KNOWING a detail — Tuesday or Emma — does not increase or decrease the chances that in a given family, the two children are either two daughters or two boys. Instead, KNOWING such a detail means that you have meet a parent which is part of a SUBSET of parents, and this is why the chances are usually bigger.
Funny thing, if in the simple case the answer is “1/3 not 1/2” and in the “Tuesday” case… ummm… something changes, now with Emma this changes back to… umm… wow.
Once Jane has a daughter Emma, what else could she have? (We suppose everything equiprobable, we won’t enter into gender statistics and stuff.) So counting the chances are easy and marvelous.
This made my Friday.
Someday Richard will post a puzzle for which the obvious answer will be the correct answer. It will confuse all the clever people, and for once I will get one right. Someday.
Hmm…
There’s an intuitive answer, based on the assumption that Emma is Jane’s daughter.
But the puzzle doesn’t state that. It says that Jane has two children, one of whom is *a* daughter. So Emma isn’t necessarily Jane’s daughter (otherwise the correct phrasing would be “one of whom is her daughter”)
After all, every female ever born is a daughter, so even if Emma was born to another mother, she would be *a* daughter…
So I guess the answer should be “It depends…” 🙂
But somehow I think Richard’s expecting a precise figure 😦
Variation:
«Jane has two children. One of them has blue eyes and the other one is a girl named Emma. What’s the probability that Jane has two girls born in a Wednesday?»
(assuming equiprobability with regards to week days and genders)
Solved it very quickly, which almost assuredly means I got it wrong. 😛
I’ve seen this puzzle before. I’ve seen the answer before. After trying for quite a while I still don’t understand it. Then again I suppose some people are equally confounded by the Monty Hall problem. It will be interesting to run a poll to find out how many people understand and/or agree with the official answer.
There’s a similar puzzle I read recently with “born on Tuesday” instead of “names Emma”. Brilliantly unintuitive answer. This one seems harder though because 1) Probability of someone being called Emma is not obvious whereas someone being born on Tuesday can be assumed 1/7. 2) Might be a problem that the probability of one child being called Emma is not independent of the probability of the other being called Emma. That is to say someone is unlikely to give two children the same name!
If this ends up being that she has a daughter that isn’t a child, i will poison your fish. Or any pets you have. Or put emetics in your salad.
I think I have the right answer… but what is so strange is that I can get the answer mathematically but not intuitively. That’s so weird to me.
See I came up with an intuitive answer, then went and read some stuff on wiki, and then plugged some numbers in and came up with the same answer. But I suspect it’s not right.
This is actually fiendishly difficult, but I had only just read a New Scientist article on “Gathering for Gardner” and remembered the apparently ‘correct’ answer. Several professional mathematicians disagree about this ‘correct’ answer, so I guess it is still ‘up in the air’!
If anyone can ‘get’ and then explain either answer, they deserve a math PhD immediately!