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It’s definitely 1/3
Christ my pretty spreadsheet has been out-nerded by some BBC Basic. Good effort!
Given the problem presented I would say it’s not possible to give an answer without knowing the facts first since it could be 0, 1/2 or 1/3 depending on which assumptions you make
This makes complete sense in my mind. Ambiguous question is ambiguous. Who’s his wife, the riddler?
Christ my pretty spreadsheet has been out-nerded by some BBC Basic. Good effort!
Sorry, just thought it made the maths a bit easier to see 🙂
The problem now is that we have no idea whether or not she found a female first or not.
It doesn't matter. Observation doesn't change the probability.
Before the phone call, there exists a certain probability that either animal is male or female. The ratio of the probabilities in relation to each other cannot change (unless the phone call was to a gender reassignment surgeon).
If we then add additional information (at least one is a boy) then we can rule out permutations we discover are impossible (they cannot both be girls) but we cannot make the remaining permutations more or less likely than each other.
If we remove all the fluff about beagles, bathing, the wife etc, the question that’s being asked is ‘there’s a canine, we don’t know it’s gender, what is the chance that it’s male?’
the other animal is irrelevant, as we know what gender it is.
There are only 2 possible answers, either it’s male, or it isn’t.
Yep, so 3 equally possible scenarios where only one scenario is both dogs are male.
No, because even if you reverse it and check dog B first that would remove options 1 and 3 leaving 2 and 4.
then we can rule out permutations we discover are impossible (they cannot both be girls) but we cannot make the remaining permutations more or less likely than each other.
Exactly. But unlike Monty Hall we don't know how the wife arrived at the conclusion "at least one is male". The answer to the question "What is the chance there are two boys?" is very much dependent on how she came to that conclusion.
Put simply, why is the assumption that she knew the sexes in order to give the 1/3 answer any more valid than the assumption she never from the data given. This ambiguity (or lack thereof) is why the Monty Hall problem works and this doesn't. Monty Hall furnishes you with those facts from the outset, this just looks like someone trying to be clever but not giving you enough facts to give an informed answer.
Ambiguous question is ambiguous. Who’s his wife, the riddler?
Not her fault really. If the shopkeeper or customer wanted to know if they were both boys then they should have asked that!
She's got the dogs to wash then she has to pick up the kids and take them to ballet, put the dinner on, and tidy the living room before the in-laws arrive for the weekend.
And all you do is sit in that shop drinking tea and asking obtuse questions about cisgendered puppies!
She should have listened to her mother.
No, because even if you reverse it and check dog B first that would remove options 1 and 3 leaving 2 and 4.
Nope. See my point about hands. You are forcing a particular dog to be in a particular "hand". We, as the shopkeeper, don't have that information even if she does.
The question is wrong.
1/3 maths is correct, as long as the two dogs are in a state of gender flux. They are not.
Exactly. But unlike Monty Hall we don’t know how the wife arrived at the conclusion “at least one is male”. The answer to the question “What is the chance there are two boys?” is very much dependent on how she came to that conclusion.
We don't care about how she came to her conclusion other than she was truthful. We should not care if she looked at one or both or indeed didn't need to look as she already knew. It's all irrelevant. To the binary question 'is one of them a boy' she gave a binary yes/no answer.
The ratio of the probabilities in relation to each other cannot change
so it is a maths question rather than common sense logic?
......asks her if there’s at least one boy. She says yes.
What is the chance there are two boys?
i really do see what the one-thirders are saying, but i just think its hiding behind the fact it asks what the chance is, after she says yes. how she finds out, either looking or knowing beforehand is irrelevant, we just have to accept that its a yes.
the issue is, we read it as 'NOW what is the chance of them both being boys then?' whereas the one-thirders are saying ignore the info youve been given, what was the chance before cos maths never changes probablities in relation to each other...... i think. which makes it a shit question 😀
so it is a maths question rather than common sense logic?
Of course it is maths question. Not sure anything is 'common sense logic'. 'Common sense logic' is just a conundrum that can be determined reliably using basic 'tools' that the average man on the street has already mastered. We presuppose what the average man on the street can get their head around at our peril. I give you Brexit. This 'riddle' requires the average man on the street to have a reasonable grasp of the mathematics of basic probability. I suggest a fair few don't have that tool to hand. Not that they are daft; just were never taught or can't remember how to do it.
so it is a maths question rather than common sense logic?
No, it is an example of how "common sense logic" will sometimes give you the wrong answer.
It's not some virtual theoretical paper-only thing. In the real actual empirical world the answer is 1/3.
we read it as ‘NOW what is the chance of them both being boys then?’ whereas the one-thirders are saying ignore the info youve been given, what was the chance before
No, that's not what we are saying.
We are saying you have to use the information you are given in the correct manner. <span style="font-size: 0.8rem;">It lets you eliminate one of the original four equally-likely scenarios. Leaving you with three equally-likely scenarios.</span>
whereas the one-thirders are saying ignore the info youve been given, what was the chance before cos maths never changes probablities in relation to each other…… i think.
No, maths as a methodology never changes but you don't ignore the data you have been given. It is vital. Just not as odds limiting as some believe. The new information changes the probability of two males from 1/4 to 1/3 from that point forward.
so it is a maths question rather than common sense logic?
There's common sense and there's logic, they're different things. The whole point of puzzles like this is to challenge our "common sense" intuition, where the correct solution flies in the face of what "feels" should be right. There's a name for this, it's called a veridical paradox.
In any case, the fact that the puzzle exists at all should ipso facto tell your "common sense" that the obvious solution is unlikely to be the correct one, otherwise it'd be a pretty pointless puzzle. If I'd posted, "you have a dog, what are the odds that it's male" then either you'd go "50%, duh" or you'd go Peak STW and start analysing global canine birthrate trends. Either way that'd just be lame.
I've skipped most of the 7 pages (wtaf) so apologies for doubtless repeating what's gone before (but given it's 7 pages long it's got to have been repeated a lot already)
The answer i's 1/3.
The chance of 1 dog being male is 50/50
The chance of any dog picked at random being male is 50/50
The second dog is not picked at random, it's a defined sample and the sample was defined before you had the info so the chances of the second dog's gender being the same as the first are lower and defined by the chances of the sample being gender combo xx
If the question was i have a dog and i sex it, i then pick another dog from the global population, what is the chance the second dog is male, the chance is 50/50 near as damn it as the sex of the first is irrelevant, but that's not the question.
The question is pick two from a global population, now in your reduced sample what are the odds you picked...
Nowhere in the riddle does it say “the sex of both dogs has been determined randomly”
Gender is determined randomly at fertlisation. The original question seems to me to say one dog is male, here is another what are the chances its male answer 50%. If it clearly said give the chance of bith dogs being male its 25%. If it said the chance of both being male if one is male but you dont know which its 33.3%
As Torminalis points out tge wording is a bit shit. I wonder if maths people look at it differently from a biologist like me and then make differentvassumptions to answer the question.
LOL. Nice back tracking @anagallis_arvensis 😆 Glad you got there in the end.
Are you with us yet @sadexpunk ?
The question can be encapsulated thus:
If you have two dogs and you know that they are not both female, what is the probability of them both being male?
The answer is 1/3.
LOL. Nice back tracking @anagallis_arvensis 😆 Glad you got there in the end.
Same as what I said this morning on page two, its poorly worded and in the absence of extra info I will go with the biological option.
If the question was i have a dog and i sex it
..then will I go to jail?
The question can be encapsulated thus:
If you have two dogs and you know that neither of them are female, what is the probability of them both being male?
The answer is 1/3.
Wha? If you know neither of them are female then they both have to be male, so 100%
in the absence of extra info I will go with the biological option.
No one suggested that the odds of any single specific dog being male was anything other than 50:50. That's very much the basis of the question.
Taking the "biological option" doesn't change the answer. 😆
Ok Graham it was page 4!! Before I had coffee this am
I dont doubt the maths but the first says 1 dog is male, whats the probability another dog is male. Thats 0.5. If you have a baby thats male the probability of the next baby being male is also 0.5, the probability of having 2 male babies is 0.25.
In his second statement where he talks about the “essence” he adds the word “also” which utterly changes the meaning.
I dont doubt his maths but do doubt his language.
..then will I go to jail?
For a long time too, the sentencing is pretty ruff.
Same as what I said this morning on page two, its poorly worded and in the absence of extra info I will go with the biological option.
I hope you’re not a teacher in Harrogate or it’ll cause a post on here.
mmm..
if i had two coins and tossed the first one and it landed heads
whats the chance that the next one lands heads, I'd have to say 50-50,
although technically its 1 in 4..
Are you with us yet @sadexpunk ?
begrudgingly so yes 🙂 AA puts it a little better than i would i think, but yep, so be it. i was sort of hoping for a eureka moment, AHAAAAAAA i get it now type thing, or to actually win and the one-thirders having a eureka moment instead, altho that was more unlikely 😀
but......its just poorly worded on purpose i spose which sadly brings the thread to a bit of a damp squib shrug yer shoulders type ending.
In any case, the fact that the puzzle exists at all should ipso facto tell your “common sense” that the obvious solution is unlikely to be the correct one, otherwise it’d be a pretty pointless puzzle. If I’d posted, “you have a dog, what are the odds that it’s male” then either you’d go “50%, duh” or you’d go Peak STW and start analysing global canine birthrate trends. Either way that’d just be lame.
yep, tis true 🙂 altho even tho thats what i thought it was asking in the first instance, i wont lie, my initial thought was 75%. you know, one dogs decided so thats 50%, now this ones got 2 choices so maybe 75%. but then again im a maffs doofus and was waaaaay out 😀
Wha? If you know neither of them are female then they both have to be male, so 100%
Thankfully mrb123 has edited his post. It now is a neat question that no doubt plenty will still have an issue with.
The question can be encapsulated thus:
If you have two dogs and you know that they are not both female, what is the probability of them both being male?
The answer is 1/3.
if i had two coins and tossed the first one and it landed heads
whats the chance that the next one lands heads, I’d have to say 50-50,
although technically its 1 in 4..
No, there it is 50:50
Before you started your chances of two heads were 1 in 4.
But once you have the result of the first toss you are now 50:50.
The difference between that and the puppies is that you know the order of the coin tosses so the new information eliminates two of the four possible equally-likely outcomes.
With the puppies you don't know the order, so you can only eliminate one of the four possible equally-likely outcomes.
Thankfully mrb123 has edited his post. It now is a neat question that no doubt plenty will still have an issue with.
Phew! Makes sense now
its just poorly worded on purpose i spose
Well, it's not my wording per se, though I did tweak it from the original to try and make it less ambiguous (IIRC the original asked, "what are the odds that the other is male" which is blatantly misleading). But I certainly didn't intend for it to be badly worded and I'm more than happy for any suggestions as to how the phrasing can be improved.
I hope you’re not a teacher in Harrogate or it’ll cause a post on here
I await my strongly worded email with much anticipation
I've encountered this problem a few times on multiple forums @Cougar. Every single time it ends with people saying "well that's just badly worded".
I think what they really mean is that their "common sense" approach misled them, therefore the question must be misleading.
I really don't think it is. You see the same responses to Monty Hall or the Plane on the Conveyor Belt.
but……its just poorly worded on purpose i spose which sadly brings the thread to a bit of a damp squib shrug yer shoulders type ending.
I think poorly worded is harsh. I'd say it is worded to allow the unwary to trip over. Not a true riddle as such as I don't think there is any ambiguity. MRB123's (edited) succinct version states it clearly but without as much fun.
However.......Cougar....tut tut. I have now read the solution linked to at the bottom of page 1 and you changed the genders of the shop keeper and the washer of dogs when you posted in the OP. Gender stereotyping right there with your male shop owner and female skivvy dog washer.
There seems to be a lot of people who didn't read the original question properly. He'll take the pups if at least one is a boy, the shopkeepers wife says that one of them is. The chances of the other being male is 50:50.
the one thing i still don't understand now is how you guys can reply to comments with the comment in the box,
when i click on reply its doesn't show the box, what am i doing wrong.
copy text, click the speech marks in the reply box which indents the cursor an inch or so. paste. then hit return twice to get cursor to start your reply.
There seems to be a lot of people who didn’t read the original question properly.
Indeed so their answer wrongly with 50/50
<div class="bbp-reply-author">whatyadoinsucka
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the one thing i still don’t understand now is how you guys can reply to comments with the comment in the box,
when i click on reply its doesn’t show the box, what am i doing wrong.
Nothing!
So, the probability of one of the dogs being male =1...
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The 'original' with a detailed explanation.
A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're both male, both female, or one of each. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. “Is at least one a male?” she asks him. She receives a reply. “Yes!” she informs you with a smile. What is the probability that the other one is a male?
https://scienceblogs.com/evolutionblog/2006/12/28/a-probability-puzzle-part-two
The chances of the other being male is 50:50.
Ah.. the question that keeps on giving. 🙂
You pick any pair of dogs randomly from the litter then, as above, you are in one of four equally-likely scenarios..
1) both dogs are male
2) the one in your left hand is male and the one in your right is female
3) the one in your left hand is female and the one in your right is male
4) both dogs are female
You learn that at least one is male. So you can discount the both female scenario. And you now know you are in one of three equally-likely scenarios:
1) both dogs are male
2) the one in your left hand is male and the one in your right is female
3) the one in your left hand is female and the one in your right is male
See?
Jeez, really? 8 pages? Bloody Nora!
I understand how each side has arrived at the maths answer or the real world/logical answer, but this made me laugh out loud in the office:
"behind one is a car and behind the other two is a goat, and you’re invited to pick one. The host, who knows where the prizes are, then opens one of the other two. He reveals a goat"
I think you’ll find he can only reveal half of one (very large) goat as there is only a single goat mentioned in the first sentence.