Her daughter: “my head hurts”.

Her other son: “waiting for 1000 comments”.

I – gave the Monty Hall problem to my husband who got hooked and started calculations. What’s the probability of a woman to start such calculations compared to a man???

BTW reminds me of the “interest in stars and 15yo. boys in girls” on the hanabi evening with our two 4th grade boys.)

Anyway this post definitely took me some time (googling). Significantly more time compared to the others.

Anne ]]>

JeffreyF’s math is correct. Still, my preferred answer remains: 100%. Why? JeffA is an adept computer programmer, is competent at english, and I suspect he knew a priori that his wording was ambiguous. I look forward the next “stack overflow” podcast to see if Jeff and Joel discuss this question.

]]>Here is an other example of the way our mind works:

One flow is intuitive and fast (sometimes right , sometimes wrong)

The other is analytical and slow (and sometimes right or wrong)

Here is the problem:

I just purchased an envelope and a stamp for $1.10

The envelope costs $1 more than the stamp

What is the cost of the stamp???

Quickly you will answer : obvious $1 for the envelope and $0.1 for the stamp , this adds to $1.10

But if you now substract , you’ll find a $0.9 difference, not a $1 as asked !!!!

I let you compute the correct answer

When intuition and analytics are in conflict, there is a little voice in our brain which tells us “it looks that way, but it’s wrong” This little voice has been experimentally measured (like in the envelope problem) and tells the truth in 95% of cases . So follow your little inner voice when it tells you “something is incoherent here”

]]>What most people seemed to be struggling with is that by randomly identifying the girl on the swing to be his/her daughter, one explicitly breaks the symmetry in the “girl then girl” pairing of the answer space.

More precisely, the answer space should include “girl-on-swing then girl-not-on-swing” and “girl-not-on-swing then girl-on-swing” in addition to “boy-not-on-swing then girl-on-swing” and “girl-on-swing then boy-not-on-swing”.

Consequently, the kid who is not sitting on the swing has a 50% chance of being a boy.

In general, we don’t know which girl of the (girl, girl) pair is randomly named as being his/her daughter by the parent.

The Monty Hall problem is different in that the revealation of the game show host depends on the prior pick of the game show contestant.

]]>> The question has nothing to do with ordering

True but the interpretation of it and modelling it via mathematical representation – has everything todo with it.

> in this context, boy/girl is indistinguishable in every respect from girl/boy

Depends on the model, if you choose to introduce some “ordering” (relation) in a pair such as “older than”, then (boy, girl) is not the same as (girl, boy).

I really am missing your point, because if you “choose to introduce some ordering” to the question, you’re then answering a different question. —Jeffrey

> This one-of-each set is not, however, equal in probability to the other sets (two boys, two girls)

It is if there is no “ordering” to the pair.

]]>I am not saying that one of them is right and one is wrong – it all depends how you choose your mathematical model. But in a simple case when there is nothing known apart from the kids gender/sex/whatever – the former model where (boy, girl) and (girl, boy) are one and the same seems to be the closes match. Adding partial ordering by age may as well be replaced by anything else similar(like ordering by height, weight etc – I don’t see why age should be preferred to anything else and used at all ðŸ˜‰

I’m not sure what you indend your point to be in the context of my post. The question has nothing to do with ordering, so there are only three types of sets under consideration, and in this context, boy/girl is indistinguishable in every respect from girl/boy. This one-of-each set is *not*, however, equal in *probability* to the other sets (two boys, two girls), and that inequality among the three members of the set is important to understanding both the question and its answers. —Jeffrey

Fowler’s Modern English Usage says: “gender (n.) is a grammatical term only. To talk of persons or creatures of the masculine or feminine gender, meaning of the male or female sex, is either a jocularity (permissible or not according to context) or a blunder.”

Your esteemed compatriot, Bill Bryson, says “Gender, originally strictly a grammatical term, became in the nineteenth century a euphemism for the convenience of those who found ‘sex’ too disturbing a word to utter. Its use today in that sense is disdained by most authorities as old-fashioned and over-delicate.”.

But I guess it is not for me to comment on anyone else’s use of English, sorry – mine is flakey enough at times!

Maybe it’s my midwestern American upbringing, but I find no need to borrow from the noun “sex” (making babies) to describe the one-or-the-other result one gets from it. I also don’t use the word “flip” to describe the obverse/reverse nature of the side of a coin, but maybe Bill Bryson does ðŸ™‚ —Jeffrey

]]>That did it for me. Having three and eliminating one is just the extreme case of this.

The “this” you’re speaking of here is the Monty Hall problem, mentioned in the first comment. Indeed, that’s a good way to think of it, but you have to remember the important point is that when “they” eliminate 998 other doors, it’s done with the knowledge of which door holds the prize, and the intent to not reveal the prize. (If they eliminate 998 doors randomly, they’ll reveal the prize 99.8% of the time, but because they know where the prize is and choose not to reveal it, they end up revealing it the desired 0% of the time.)

None of this is directly related to the two-kids problem discussed in the post, though. —Jeffrey