Seeing as this is currently breaking Facebook…

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