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im sticking to what we’ve been told about these 2 dogs. ones male, whats the chances of them both being male then. 50/50
Riddle me this. I have a big bag of balls. 50% are red, 50% are blue. You close your eyes, pick out two at random and hold them in your closed fists. What are the odds of them both being red?
The ball in your left hand could be red or blue. 50% chance of either. The ball in your right hand could be red or blue. 50% chance of either. So our possibilities are,
You have a red ball in both hands.
You have a blue ball in both hands.
You have a blue ball in your left hand and a red ball in your right.
You have a red ball in your left hand and a blue ball in your right.
Each permutation equally possible, 25% chance of each. Yes?
I then look at them and tell you "at least one of them is red." What are the odds of them both being red now?
You now know that both cannot be blue. But you cannot rule out any of the other options. Of the three equally likely permutations, one states that they're both red. Observing them does not change the probability, they're balls (or dogs) not quantum particles.
but why do you need to keep the original odds the same? the odds have now changed, as we now have more info.
How does the new information change the 50:50 likelihood of any single dog being girl or boy? It doesn't.
It might make a little more sense if you think about the odds improving, not getting worse.
Before you have any information there is a 1/4 chance that they are both boys.
Once you know that at least one is a boy then you know there is a 1/3 chance they are both boys.
im not looking at it as improving or getting worse. and you may be right to the laws of mathematics, i dont know, im not good enough at maths to check that bad boy out. to me, the question doesnt mention 'using the laws of mathematics, what is the probablity......', it just gives us a scenario, to which the answer is 50/50 😀
No-one has said or even implied the first dog/coin has been randomly determined. It could have been selected precisely because of what it is. So you'd be better of saying, coin A has been PLACED heads up. Coin B is tossed. What is the probability of both coins being heads. Still think it's 1/3?
but why do you need to keep the original odds the same? the odds have now changed, as we now have more info.
The odds of there being two females or not being two females - the ratio between those two outcomes - has changed, yes.
However, the odds of their being either one male or two males - the ratio between those two outcomes - has not.
How does the new information change the 50:50 likelihood of any single dog being girl or boy? It doesn’t.
thank you. the likelihood of that dog being male is 50/50 as you correctly say. so as we know the first dog is male.....
Riddle me this. I have a big bag of balls. 50% are red, 50% are blue.
no no no no noooooo...... lets keep to the original question, i can understand that. why do we have to keep going to doors, coins, balls etc??
I'm making a list of who is in my gang.
@sadexpunk - the error you are making is that you assume the wife knows which one is male and which one she hasn't checked. That isn't the case with the wording of the question so MF & FM are different meaning that MM is one of three options.
So you’d be better of saying, coin A has been PLACED heads up. Coin B is tossed. What is the probability of both coins being heads. Still think it’s 1/3?
No, because again, that is a different question. Nowhere in the riddle does it say "you arbitrarily choose one dog and declare it to be male." You're changing the puzzle to fit your solution. Stop it.
@sadexpunk – the error you are making is that you assume the wife knows which one is male and which one she hasn’t checked.
we keep going back to the crux of the matter, which is where it will be won or lost.... it doesnt matter which she has checked, one or both, she may even know that there are two males, but she answers 'at least one is male'.
Nowhere in the riddle does it say “the sex of both dogs has been determined randomly” You’re changing the puzzle to fit your solution. Stop it.
so as we know the first dog is male…..
We. Do. Not. Know. This. You're adding information which isn't there. Where's this "first" dog come from?
lets keep to the original question, i can understand that. why do we have to keep going to doors, coins, balls etc??
Because you demonstrably don't understand the question, you just think you do. Go through the balls question, tell me where you think I've gone wrong.
So you’d be better of saying, coin A has been PLACED heads up. Coin B is tossed. What is the probability of both coins being heads. Still think it’s 1/3?
No, because again, that is a different question. Nowhere in the riddle does it say “you arbitrarily choose one dog and declare it to be male.” You’re changing the puzzle to fit your solution. Stop it.
but its the same as looking at both coins, seeing that one of them is a head, placing it down heads up, and then asking the probablity of them both being heads? 50/50.
Nowhere in the riddle does it say “the sex of both dogs has been determined randomly”
How else would you determine it? Is the shopkeeper a genetic scientist on the side? Good grief.
It's not a trick arcane "laws of mathematics" question. It is empirical reality as the spreadsheet shows.
Look you've agreed that if we do this 1000 times then at the start we have roughly 250 scenarios where both are boys and 750 scenarios where they are either both girls or mixed.
If you picked any one scenario at random from that pot then you'd have a 250 in 1000 chance (1/4) that it was a both boys scenario.
So once we have the new information that they are not both girls, we are left with a pot containing 250 scenarios where they are both boys and 500 scenarios where they are mixed gender.
Which scenario are we in? Well the chance that we are in a both boys scenario has improved to 250 in 750 (1/3) but it is still twice as likely that we are in a mixed gender scenario.
the probability of the second dog being male is 50% but that isn’t what is being asked. MF & FM are valid and separate probabilities so have to be taken in to account since we don’t know which of the two dogs was checked for gender.
It is whats being asked. One dog is male. the other dog is M or F the order is irrelevant.
We. Do. Not. Know. This. You’re adding information which isn’t there. Where’s this “first” dog come from?
ok, so it may not be the first dog, its a dog. but its male. so the odds of them both being male now we know this ones male is 50/50. which is where i can see your argument from. at first, before any info is known, youll be correct about the probability. but we're asked the probabliity after we know one is male.
but its the same as looking at both coins, seeing that one of them is a head, placing it down heads up, and then asking the probablity of them both being heads? 50/50.
Excellent, now we're getting somewhere. This is precisely where you're going wrong. Go get a couple of coins, try this, and report back.
If you toss two coins, see that one is a head and put it aside, the probability that both are heads is NOT 50:50. Either coin could be a head. You'll throw two heads, a head and a tail, or a tail and a head with equal chance.
Read the analysis of ambiguity in the wikipedia page about this problem.
The paradox occurs when it is not known how the statement "at least one is a boy" was generated. Either answer could be correct, based on what is assumed.
However, the "1/3" answer is obtained only by assuming P(ALOB|BG) = P(ALOB|GB) =1, which implies P(ALOG|BG) = P(ALOG|GB) = 0, that is, the other child's sex is never mentioned although it is present. As Marks and Smith say, "This extreme assumption is never included in the presentation of the two-child problem, however, and is surely not what people have in mind when they present it."
https://en.wikipedia.org/wiki/Boy_or_Girl_paradox
I'm sticking with 50/50. good luck chaps!
In your "fixed" coin tossing example you've made a mistake. (another one but it's different)
You've already tossed the first coin so the chances of it being heads was 50% you've then ignored that and stated that the probability of both coins being heads is purely down to the probability of the second coin being heads.
@ whitestone, yep Green is the reason the house always wins at roulette,
calling red or black is near enough a 50 50 chance, calling red twice in a row is 1/4 odds, calling red then black is 1/4 odds. Green just guarantees its not 50/50 at all
so the odds of them both being male now we know this ones male is 50/50
No it's not.
Pick up any pair of dogs and there are 4 possible 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
If you are told that "at least one is male" then you are in scenario 1, 2,or 3.
All are equally likely so it is a 1/3 chance you are in scenario 1.
That is very different from being told that "the dog in your left hand is male".
Then you could only be in scenario 1 or 2 so then and only then it would be 50:50
the odds of them both being male now we know this ones male is 50/50.
Again, you're singling out a specific dog and ignoring the fact that the male dog could be the other one. We do not know that "this" dog is male, at no point has the shopkeeper's wife identified a specific animal.
Let's try it this way.
A man sees a sign in a window advertising a kitten and a puppy for sale. He goes in and tells the shopkeeper he will only take the animals if there’s at least one boy.
The shopkeeper phones his wife who is bathing the animals and asks her if there’s at least one boy. She says yes.
What is the chance there are two boys?
Your argument is "we know the puppy is male so the kitten must be male or female." But we don't know that, we only know that one of them is. We could have a male puppy and a female kitten, a male kitten and a female puppy, or both males. Three possibilities, each equally likely.
You have a litter of dogs, the sex of which is determined (by observation, gene splicers not required 🙄 ) You pick one which you know to be male, and one other. Good grief, it ain't rocket surgery 😂How else would you determine it? Is the shopkeeper a genetic scientist on the side? Good grief.
You pick one which you know to be male, and one other.
Nope.
That is a specific dog. You pick any pair of dogs randomly from the litter then, as above, you are in one of four 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
..etc
Then you are told that "at least one is male" so now 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
If nothing else this thread shows why people who understand probability and can derive the correct model based on a situation, even if that model isn't the intuitive obvious one, can MAKE MONEY APPLYING IT!
there's a healthy return to be made of y'all think the return of a situation is 50%, but really it only comes up 33% of the time.
not that the international mathematicians' puppy trading market is huge & lucrative, but its possible these misunderstandings and failures of gut feelings happen elsewhere too...
For those saying it doesn't matter which one was checked:
1 A - M B - M
2 A - M B - F
3 A - F B - M
4 A - F B - F
There are two possible assumptions here that affect the outcome of the problem. The first, as per Monty Hall, assumes the wife has knowledge of the dogs genders before checking and so checking is unnecessary. If at least one dog is male then line 4 is automatically discounted. That leaves three possibilities as to the assignment of gender for each dog. 1/3 (just got that there writing it out).
The second is that she has no knowledge of the genders so has to check the dogs individually, the first check is 50/50 as to whether the dog will be male or female and determines the outcome of the overall problem. Assume the first dog (A) she checks is male, options 3 and 4 are removed leaving only options 1 and 2, the chances then of the second dog being male being 1/2. Of course dog A could have been female, options 1 and 2 are removed leaving only options 3 and 4. From the answer given, had this been the case, then the chances of the other dog being male is zero since we first found a female and we know at least one is a male. The problem now is that we have no idea whether or not she found a female first or not.
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 with the limited (in that we are never told if she knows the genders beforehand) information given.
Which is also a fantastic analogy for Brexit.
IMO
The problem now is that we have no idea whether or not she found a female first or not.
Yep, so 3 equally possible scenarios where only one scenario is both dogs are male.
It's definitely 1/3
Just to add, this is NOT the same as Monty Hall as the problem is utterly reliant on the host knowing what is behind each door for the justification to work. Since we are never told this then the stated problem has multiple answers. Much the same as asking what the square root of nine is without stating what number systems are being used if we are to arrive at a single answer.
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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<div class="">Member</div>
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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...
</div>
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.
aaaargh! The 'maths answer' is the real world logical answer! Never play poker for money.
A shopkeeper says she has two new baby beagles to show you
Have you learnt nothing!
See?
You're using the four outcomes of one scenario (unknown dogs) to try and prove the outcome of a totally different scenario (1 dog is known).
The question is still wrong.
a totally different scenario (1 dog is known)
Okay @sbob, then enlighten me. You have one dog in each hand. You’ve been told that at least one of the dogs is male but you don’t know which.
What are the possible combinations of dog genders and hands? List them.
aaaargh! The ‘maths answer’ is the real world logical answer! Never play poker for money.
played last night and won £25 actually!
I say real world and maths answer, but to me, if i am physically presented with these two dogs and am told one is a boy and the other is unknown i only need to physically check one of them to find out what sex both of them are...