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It isn’t about math or stats. It is logic and language.
Okay, using logic, list the possible gender combinations of Dog A and Dog B, given that you know they are not both female?
You also said try calling them Ishmael and Leslie
That was more an attempt at humour and probably just confused matters. Ishmael and Leslie are just synonyms for the dog that is male and the dog that is either. It does not matter which is which.
I tried creating a new model
And you failed because you are still dissecting the problem into two (or three!) parts that happen one after the other. This is not the case.
We know one of the dogs is male.
We know the other dog is either.
It doesn't matter which is which, it changes nothing.
This is another case of not seeing the wood for the trees.
Okay, using logic, list the possible gender combinations of Dog A and Dog B, given that you know they are not both female?
Dog A or B is male.
The other is male or female.
The word you are incorrectly using in your logic is "if".
There is no "if", there is only "is".
Okay, using logic, list the possible gender combinations of Dog A and Dog B, given that you know they are not both female?
Is that what the question is asking, or is it asking what is the probability of 2 out of two dogs being male given that 1 out of the 2 dogs is male?
That was more an attempt at humour and probably just confused matters. Ishmael and Leslie are just synonyms for the dog that is male and the dog that is either. It does not matter which is which.
Except it very much does. As I explained with Ishmael and Leslie. All you know is that there is at least one male. So the possibilities are:
1) Ismael is male and Leslie is male
2) Ismael is male and Leslie is female
3) Ismael is female and Leslie is male
What you are trying to do is say “Ishmael is definitely the male dog so we can discount scenario 3”.
That is using knowledge you do not have.
And you failed because you are still dissecting the problem into two (or three!) parts that happen one after the other.
Nope. Start from the point where you have a dog in each hand and I tell you they are not both girls. What are the possibilities? List them.
No dissection or steps or temporal aspect required. Just tell me the possible combinations.
The word you are incorrectly using in your logic is “if”.
You have literally just quoted me not using the word “if” then told me off for using the word “if”.
Stop using the word “flamingo” please. That is where you are going wrong. 🤪
Is that what the question is asking, or is it asking what is the probability of 2 out of two dogs being male given that 1 out of the 2 dogs is male?
It is the same answer.
List all the combinations where at least one dog is male. There are three. Only one of those combinations is male-male.
(Going to bed. Have fun)
You are not grasping the subtle but important difference. If the question is phrased in such a way that it forces you to address the dogs as a pair (the pair being a singular unit with the characteristics of MF, MM, FM and FF) then the punnett square solution you are fixated on is appropriate. If the question is phrased so that it simply asks about 2 individual dogs, each as it's own singular unit having only one possible characteristic of M or F then your approach doesn't work.
The original wording of the problem does this. The changed wording does not.
Start from the point where you have a dog in each hand
That point does not exist.
You have literally just quoted me not using the word “if” then told me off for using the word “if”.
Sorry, I thought in relation to logic it was obvious.
What you have been saying all along is that if the dog in your left hand is male then the dog in your right is male or female, and if the dog in your left is female then the dog in your right is male which gives you your three options.
This is where you have been going wrong. There is no if, no one then the other because as soon as you consider one it changes the odds of the other which is not dictated in the original conundrum.
There are two dogs, one is male, the other is male or female.
Inside Sbob's head.
Inside STW:
Why is it that the homepage shows this thread at 12 pages, but this is page 13?
It's a forum feature.
The most glaring and easily understandable change is from “what are the chances of the other one being male” to “what are the chances of the other one also being male”
This what I said pages and pages ago. The explanation in the link adds the word also which utterly changes the question. Its badly word, or very well worded, depending on what its trying to achieve.
Can I check I have the gist of the argument correct?
It's not about the maths, it's about whether the question is a linguistic trick or a slightly ambiguously worded maths puzzle?
I'd ask sbob to flip a coin a hundred times and pair the results, but he'd tell me he should actually be given a coin that's already heads and flip another one to see if it matches.
I don't think the use of the word "also" changes the meaning in any way
"the other one being male" already refers to the one other than the one that has been determined to be male, thus is perfectly synonymous (in this context) with "the other one also being male".
One on my shoes is wet. If the other one is wet, then it is also wet.
It’s not about the maths, it’s about whether the question is a linguistic trick or a slightly ambiguously worded maths puzzle?
Yes, the original puzzle is a maths probability problem with a clear answer (albeit the answer is counterintuitive, hence the heated discussion). Some people who don't agree with the correct answer and explanations are attempting to justify wrong answers by arguing about language or answering different questions!
I don’t think the use of the word “also” changes the meaning in any way
No not at all it just makes it clearer for those that can’t grasp the original question. Me included when it first appeared on here waaaay back.
I don’t think the use of the word “also” changes the meaning in any way
It certainly clarifies what the question is asking you, obviously if you read it correctly and understand the maths you get the correct answer. My problem when always doing these problems is that I know I am supposed to be tricked, get bored reading about puppies (I prefer playing with them) and skip to the end as I really am not bothered about getting it right or wrong.
What might be an idea now, is to change the question so that everyone (might) get the same answer. Keep the original question the same, but make the probability of a male dog be 2/3 and female dog 1/3.
What might be an idea now, is to change the question so that everyone (might) get the same answer. Keep the original question the same, but make the probability of a male dog be 0.666666 and female dog 0.333333
I'm slightly dissapointed with you given your username
I’m slightly dissapointed with you given your username
Whilst this does not surprise me - I frequently disappoint. Could you explain further. And I didn’t use decimals, as that would not give the same answer ie 1/2.
Gaussian distribution joke init? Yes that's where we are.
I'm genuinely disappointed no one's tried to explain the alternative solution using Bayes' Theorem. Which gives the same answer of course. It's straightforward logic, this isn't one where we get to vote.
gaussian distribution joke init? Yes that’s where we are
Hmm, I’m more of an admirer of Gauss than a peer. Somewhat out of my comfort range, but I’d still chose fractions over decimals in most situations, as a preference.
I’m genuinely disappointed no one’s tried to explain the alternative solution using Bayes’ Theorem. Which gives the same answer of course. It’s straightforward logic, this isn’t one where we get to vote.
Whilst I’ve heard of Bayes’ theorem, I know nothing more about it than:
Bayes' theorem is a formula that describes how to update the probabilities of hypotheses when given evidence.
So I had a quick look online and the first site I looked at https://brilliant.org/wiki/bayes-theorem/ does just that. Quelle surprise 1/3.
Hah, that page even uses the same example.
We might reason as follows: “We know that one is a boy, so the only question is whether the other one is a boy, and the chances of that being the case are 50%. So again, the answer is 50%"
This makes perfect sense. It also happens to be incorrect.
How many children does the woman who's bathing puppies have?
The main thing conveyed by this thread is just how far people will go to not "lose" an argument. Inverted commas 'cause learnin' ain't losin'.
When will this be finished?
I’ve got a fiver each way on the Beagle in trap 2.
Got good odds .....3/2
Guys I may not be an egghead maths guy like you lot but listen, I’ve got plenty of qualifications in common sense from the university of life and here’s my take...
the wife picks up the male dog
there is one dog left
that dog has a 50/50 chance of being a male.
Answer is 50% - qed end of thread
hope this helps some of you
that's answering a different question.
anyway... which one is the Nazi? The shopkeeper or the one washing the dogs?
We know one is a Beadle of the male variety. What’s the odds of the other one also being a male Beadle?
The 1/3ers cannot cope with applying all their information at once, as garnered from the question.
They would be the people looking at the ever decreasing steps taken by Achilles in Zeno's famous paradox completely failing to realise that the tortoise would be overtaken.
You can keep your paradox pal
all I know is, a man rings his wife and asks her if she’s holding a dog. She says yes, it’s a boy. He then asks her what the other dog is and she replies that it’s 50% a boy too.
Whilst this does not surprise me – I frequently disappoint. Could you explain further. And I didn’t use decimals, as that would not give the same answer ie 1/2.
Because in all honesty* i read it as 1 in 3 which isn't a probability.
I was trying to be smart and itbackfired what is the probability of this occuring again ...
*Words are hard
What’s the odds of the other one also being a male Beadle?
On the one hand, quite large, on the other.....😉
Guys I may not be an egghead maths guy like you lot but listen, I’ve got plenty of qualifications in common sense from the university of life and here’s my take…
I’m sorry, but all your qualifications in common sense (I’m not sure there actually is such a thing) aren’t worth the paper they’re not written on.
Safe to say, maths trumps all else.
It’s one thing to not be a “maths egghead”, but to argue with people who know what they’re talking about, doesn’t holler much sense at all.
On the one hand, quite large, on the other…..😉
Dead uncertain.
The 1/3ers cannot cope with applying all their information at once, as garnered from the question.
Go on then. I'll bite one more time. Where is the flaw here:
You have let's say 10,000 pet shops in your town. Each with a random number of dogs of a random distribution of genders.
For example there will be approximately 100 shops with 1 dog, split roughly 50 M, 50 F. There will be approximately 100 shops with 2 dogs split roughly 25 MM, 50 MF, 25 FF. There will be approximately 100 shops with 3 dogs split 12 MMM, 38 MMF, 38 MFF, 12 FFF and so on... Do you agree this is a fair random distribution?
We only care about shops with two dogs where one is a male. That is 75 shops out of the 10,000. If you randomly phone one of those shops what is the probability that they have 2 males? Pretty clearly there are 25 shops with 2 males so 25/75 or 1/3
The 1/3ers cannot cope with applying all their information at once, as garnered from the question.
They would be the people looking at the ever decreasing steps taken by Achilles in Zeno’s famous paradox completely failing to realise that the tortoise would be overtaken.
Or, more likely the ones who know how to sum an infinite geometric series!
This is starting to get irritating now. Do any of the 50%ers have an area/topic on which they know what they’re talking about. I’d like a go at coming along and talking shite.
Is the question actually answerable until you have determined that Beagles are actually born at an exact 50:50 ratio of female - male?
Safe to say, maths trumps all else.
Only if you use the correct maths.
wow is this still rumbling on, i thought it was decided yesterday that the second dog is male is 50:50
but the probability of both dogs being male is 1 in 3 (as no FF option as we know one is a male)..
it all depends how you read the question and if you feel the other dog is dependent or independent of the outcome..
Is the question actually answerable until you have determined that Beagles are actually born at an exact 50:50 ratio of female – male?
Yes, but you need to know the ratio to get a value. 50:50 gives 1/3
Because in all honesty* i read it as 1 in 3 which isn’t a probability.
Why not?
What is wrong with the probability of rolling a 5 on a fair, standard, 6 faced die, being 1/6?
wow is this still rumbling on, i thought it was decided yesterday that the second dog is male is 50:50
but the probability of both dogs being male is 1 in 3 (as no FF option as we know one is a male)..
Whoa there! What are you doing with the being sensible? I’m trying to get this bad boy to 20 pages.
The fact of the matter remains that there are two dogs; one male, one male or female. There is no point in talking about a female dog that does not exist in the question.
wow is this still rumbling on, i thought it was decided yesterday that the second dog is male is 50:50
but the probability of both dogs being male is 1 in 3 (as no FF option as we know one is a male)..
it all depends how you read the question and if you feel the other dog is dependent or independent of the outcome..
Arghh! There is no ‘second dog’.
The fact of the matter remains that there are two dogs; one male, one male or female. There is no point in talking about a female dog that does not exist in the question.
In your world this might be the case. That is to say a construct which has be colluded to ensure the series of events described is the only possible outcome to the point in the 'story' where the wife answer yes with the only probability left to consider is the final play.
I think your view of the problem is flawed. I can see how you could hold it, but don't think it rational. Your engineering of the scenario to ensure that the outcome is the same no matter how many times is plays out alters the probability irrevocably.
There are a lot of us here.
each of us phone the local pet shops until we find one which has 2 of one particular breed of animal.
Report back here the sex of each
should prove it once and for all.
I went past the local pet shop,the other day. They had a sale on.
All the budgies were going cheep.
IGMC .
Well, given the fact that this thread is at 14 pages and counting, trying to argue and reason this out seems to be working really well.
TIME FOR EXPERIMENTATION!!!
Take a deck of playing cards and remove all the cards for two of the suits.
This will leave you with 13 cards represented by your girl suit (for arguments sake, let's say hearts) and your boy suit (spades)
1. Shuffle the 26 cards and deal two cards, the first one face up
2. If the card is a heart (girl), return the cards to the deck and shuffle again
3. If the card is a spade (boy), turn the next card face up
4. Make a note of whether the 2nd card is a boy or girl
5. Repeat until you get bored
I did the above 30 times and my results were:
18 girls, 12 boys
If everyone does this a few times and logs their results we can keep a running total. If the 50% people are correct the numbers should converge back to an even distribution pretty quickly. If the 1/3 people are correct the numbers should swing the other way.
I went past the local pet shop,the other day. They had a sale on.
It’s a wonder it didn’t blow away...... or is that the paper shop?
I'm doing the opposite of engineering the scenario, I'm looking at the question as is.
The 1/3rd answer is the engineered dissection.
As I said earlier, this isn't about the maths, it's about how one's brain deals with information. On one hand there is a group assessing all the information at once, on the other there is a group that has to break down the information to make sense of it.
You have: if dog 1 = M, then dog 2 = M or F coupled with If dog 1 = F, then dog 2 = M, giving the three options.
or
You have a dog which is male and the other that is male or female.
I can quite easily see how the former is more attractive to a certain type.
1. Shuffle the 26 cards and deal two cards, the first one face up
2. If the card is a heart (girl), return the cards to the deck and shuffle again
Nope, this is still broken logic. You're arbitrarily assigning "male" to the first card / dog. The second card / dog could be male and it would meet the criteria in the puzzle but you've just rejected it.
1. Deal both cards face up.
2. If both cards are hearts (girls), return the cards to the deck and shuffle again
TIME FOR EXPERIMENTATION!!!
Your experiment is as flawed as the earlier coin toss suggestions. They both produce results that do not fit in with the question therefore are not valid.
2. If both cards are hearts (girls), return the cards to the deck and shuffle again
I suppose you think we should be having a second referendum, you know, until we get the result that we want?
As I said earlier, this isn’t about the maths, it’s about how one’s brain deals with information.
You're not wrong there.
The whole point is that the solution is counter-intuitive. The question then becomes whether you can override your gut feelings in the face of explanations and facts, or whether you doggedly cling to what "feels right" and start twisting the original premise to make it fit.
I suppose you think we should be having a second referendum, you know, until we get the result that we want?
We had a second referendum in 2016.
I'm impressed all of this is still going.
Surely it's about semantics - how the question is asked.
[b]The 50/50 explanation:[/b]
Man phones wife, and says "is one of those two dogs male?"
She says "yes."
He asks "is the other one also male?"
Probability of her replying yes: 50%
(assuming dogs are equally likely to be born female as male)
[b]The 1/3 explanation:[/b]
Man phones wife, and says "is one of those two dogs male?"
She replies "neither is female."
Probability of both dogs being male: 1/3
(because there are 3 possible situations: dog A is male and B female, dog A is female and B male, dog A is male and B is male)
HTH.
She replies “neither is female.”
Probability of both dogs being male: 1/3
erm?
I’m impressed all of this is still going.
Surely it’s about semantics – how the question is asked.
<strong class="bbcode-strong">The 50/50 explanation:
Man phones wife, and says “is one of those two dogs male?”
She says “yes.”
He asks “is the other one also male?”
Probability of her replying yes: 50%
(assuming dogs are equally likely to be born female as male)
<strong class="bbcode-strong">The 1/3 explanation:
Man phones wife, and says “is one of those two dogs male?”
She replies “neither is female.”
Probability of both dogs being male: 1/3
(because there are 3 possible situations: dog A is male and B female, dog A is female and B male, dog A is male and B is male)
HTH.
was going to say clearest post yet til
She replies “neither is female.”
Probability of both dogs being male: 1/3
erm?
but yes, amend that to "theyre not both females" and its perfect?
I’m doing the opposite of engineering the scenario, I’m looking at the question as is.
The 1/3rd answer is the engineered dissection.
As I said earlier, this isn’t about the maths, it’s about how one’s brain deals with information
It's maths probability problem, and there is only one correct answer to the question "as is".
Lots of people on this thread have explained the answer. You can find independent explanations of the problem elsewhere. You can easily simulate the problem yourself and actually check the outcome. The only reason to continue arguing against the correct answer, or to keep changing the original problem, is that it's more important to convince yourself you are right than it is to understand something.
I didn't get the correct answer when I first looked at it, but I read the explanations that people provided, reread the question and worked it through myself. Now I've learned (or relearned; it's a long time since I studied any probability) something. There's nothing wrong with being wrong if you learn from it!
This:
I’m doing the opposite of engineering the scenario, I’m looking at the question as is.
The 1/3rd answer is the engineered dissection.
As I said earlier, this isn’t about the maths, it’s about how one’s brain deals with information. On one hand there is a group assessing all the information at once, on the other there is a group that has to break down the information to make sense of it.
You have: if dog 1 = M, then dog 2 = M or F coupled with If dog 1 = F, then dog 2 = M, giving the three options.or
You have a dog which is male and the other that is male or female.
I can quite easily see how the former is more attractive to a certain type.
reminds me, of this:
“Doublethink means the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them.”
The whole point is that the solution is counter-intuitive. The question then becomes whether you can override your gut feelings in the face of explanations and facts, or whether you doggedly cling to what “feels right” and start twisting the original premise to make it fit.
Was the question worded in such a way that it sounds similar to a logic puzzle, one that has a non-intuitive answer, but has been re-worded so that the intuitive answer is the correct one?
It was the bit about the bath that suckered me in.
I guess the original version was something like, 'Hey, is that dog you're bathing a boy or a girl?'
There are a lot of us here.
Some of which have returned from a year long slumber just to post on this thread.
It’s a good thread Drac
reminds me, of this:
One of favourite books!
Later that evening the man is washing his mountain bikes. What are the odds one is an e bike and the other is a rigid 29r?
Later that evening the man is washing his mountain bikes. What are the odds one is an e bike and the other is a rigid 29r?
On what day did he purchase the e-bike?
On what day did he purchase the e-bike?
Oh, you really don't want to go down that road. If this puzzle was confusing, that probability will break everyone's head.
She replies “neither is female.”
Probability of both dogs being male: 1/3
(because there are 3 possible situations: dog A is male and B female, dog A is female and B male, dog A is male and B is male)
Perhaps I should have emphasised, probability of [u]both[/u] dogs being male: 1/3. If they're not female, they're male (we're assuming... let's not get into trans politics!)
So probability of [u]only one[/u] dog being male is 2/3 (2 out of the three situations I described with dogs A and B), probability of [u]both[/u]/ (the 3rd situation) is 1/3.
Does that make more sense?
On what day did he purchase the e-bike?
The day that hell froze over!
each of us phone the local pet shops until we find one which has 2 of one particular breed of animal.
I gave it a try at my local pet shop. They have an ant farm and pulled two out for me. Turns out there are hardly any female Beagles. Most are worker beagles but there are a few male beagles around July.
Don't know if anyone has already linked to Marilyn vos Savant's explanation?
https://en.wikipedia.org/wiki/Marilyn_vos_Savant#%22Two_boys%22_problem
The confusion arises here because the bather is not asked if the puppy he is holding is a male, but rather if either is a male. If the puppies are labeled (A and B), each has a 50% chance of being male independently. This independence is restricted when at least A or B is male. Now, if A is not male, B must be male, and vice versa. This restriction is introduced by the way the question is structured and is easily overlooked – misleading people to the erroneous answer of 50%.
Some of which have returned from a year long slumber just to post on this thread.
Hi! Long time listener, not very regular caller; occasional lurker. Actually got a notification because someone had sent me a message, then spotted this thread. 🙂
What is the probability that the <i>other</i> one is a male?
What is the chance there are two boys?
To me, these seem to be two different questions. The first question steers towards 50pc the second towards 33pc. I'm sure they're not intended to be, but that's how I read it.
I can't help but think the arguments in this thread are more about English than maths.
I'm bored enough to have a go at explaining now. Will try to put it in 'common sense' terms for sbob's benefit.
1. Man is talking to pet shop about 2 dogs. At this point in time he has no additional information.
2. This gives 4 possibilities for their genders, 2 for each dog. There's a 50% chance the dogs are the same gender and 50% chance they're different.
3. The pet shop owner's wife then gives us an additional piece of information: 1 of the dogs is male.
4. This removes one of the 4 possibilities (both female) leaving us with 1/3 chance they're both male.
It's not about considering all the information at once or breaking it into steps. The only difference that makes is how you make sense of it in your own mind. You can skip the first 2 steps and the answer is the same. You can't change the outcome of a demonstrable mathematical problem by thinking about it differently.
You can’t change the outcome of a demonstrable mathematical problem by thinking about it differently.
You can't. But you can misunderstand the mathematical problem itself by assuming that your one way of interpreting it from the outset is the only correct one.
Read my post above with the two explanations. The two interpretations give situations that are two different mathematical problems:
One is basically "We have determined Dog A is male; what are the odds that Dog B is male?" Answer: 1/2.
The other is "We have determined that there are four equally possible outcomes and have eliminated exactly one. What is the probability that Dog A and B are both male?" Answer: 1/3