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You are all correct but this isn't mathematical logic or statistical conundrum, nor does it have anything to do with flipping coins or opening doors. This is simply a matter of interpretation of the English language and subsequent assumptions made.
From the OP, the relevant part is, and I quote, "asks her if there's at least one boy. She says yes."
We don't know whether the wife has checked one animal or both.
The 33 percenters are assuming she only checked one and are assuming MF and FM as different options because of this; whereas the 50 percenters are assuming both animals are checked and MF & FM are the same thing.
Maybe the 33 percenters are fundamentally lazy types who only do the absolute minimum amount of work whereas the 50 percenters are hard-working but inefficient types who like to dot all the "i's" and cross all the "t's"...
We don’t know whether the wife has checked one animal or both.
We don't need to know. The information provided here is "they aren't both female." Observation does not change the probability distribution.
What are the odds before the question was asked?
What are the odds after the question was asked?
Whilst I know categorically that I am a lazy toad and that I seldom dot or cross anything it has got very little to do with the answer being right. Cos I am.
Cougar: you've just proved exactly the point I'm making...you're just as guilty as jumping to assumptions as everyone else.
Your applying a very tight definition of logic which no doubt works in your world but isnt the same as the real world...
😉
Your applying a very tight definition of logic which no doubt works in your world but isnt the same as the real world…
That's the point it's a probability question in the real world the question would not be asked or then replied like that, you're changing the question and reply to get you answer.
That’s the point it’s a probability question
Is it? Where does it say that in the OP?
Again, assumptions which I'm guessing (assuming!) the mathematicians amongst us are getting their knickers in a twist about...
😉
I suspect something got lost in the translation because these types of riddles relay on very careful phrasing. What this one wants you to do is:
Man will buy dogs if :
Out of MF FM MM FF only FF is false. Therefore 3/4 odds he walks out with 2 dogs. Out of MF FM MM, what are the odds of MM? Why 1/3 obvs.
However the riddle is not written in a way that forces both MF and FM to be a possiblity. If it asked instead what are the chances the wife washed a male dog followed by another male dog then that forces that choice.
As it is written man will buy 2 dogs if Mx is true. M is true therefore the question becomes what is the probability that MM is true. That is 100*1/2. There is nothing that forces the inclusion of both MF and FM as being false
Equally the coin toss example is only useful if you define if order is important.
What are the chances of getting at least one tail in a 2 coin toss - one out of two twice - 1/2*1/2 or TT TH HT HH = 3/4? or both?
For some good explanations of the Monty Hall Problem (including some nice diagrams) read the Wikipedia page.
The "trick" I had to get my head around for the dog problem is that the wife is not giving you as much information as you think she is. The natural assumption when you first read the problem is that she is telling you that dog A is male, and dog B could be either gender, hence 50% chance of two males. In fact she is telling you that dog A and dog B are not both female, which is a very different piece of information. As others have pointed out, you don't actually know the gender of either dog, hence the three possible outcomes.
But the way it is written it doesn't matter what dog A or dog B is. All that is necessary is that one of dog A and dog B is male and what are the odds that dog A and B are both male. Since we know one of dog A and B is male then it's 1/2 that the other of the pair is male.
I suspect something got lost in the translation because these types of riddles relay on very careful phrasing.
It does which is why I use to struggle as I have dyslexia so didn't get the wording.
But the way it is written it doesn’t matter what dog A or dog B is.
It's because it is not specific that it matters.
Has the man bought the beagles yet?
Which beagle?
Jeremy
Is he about?
It’s because it is not specific that it matters.
As I said, careful wording. I looked it up and the original version of this that goes with the answer being proposed doesn't say "what is the chance there are two boys" it says "what is the probability that the other one is male". Something got lost in the translation allowing for both interpretations to be correct.
.
I suspect something got lost in the translation because these types of riddles relay on very careful phrasing. What this one wants you to do is:
Man will buy dogs if :
Out of MF FM MM FF only FF is false. Therefore 3/4 odds he walks out with 2 dogs. Out of MF FM MM, what are the odds of MM? Why 1/3 obvs.
However the riddle is not written in a way that forces both MF and FM to be a possiblity. If it asked instead what are the chances the wife washed a male dog followed by another male dog then that forces that choice.
As it is written man will buy 2 dogs if Mx is true. M is true therefore the question becomes what is the probability that MM is true. That is 100*1/2. There is nothing that forces the inclusion of both MF and FM as being false
Equally the coin toss example is only useful if you define if order is important.
What are the chances of getting at least one tail in a 2 coin toss – one out of two twice – 1/2*1/2 or TT TH HT HH = 3/4? or both?
As I said, careful wording. I looked it up and the original version of this that goes with the answer being proposed doesn’t say “what is the chance there are two boys” it says “what is the probability that the other one is male”. Something got lost in the translation allowing for both interpretations to be correct.
There would be some merit in anything you typed if the question had said that the wife was asked to look at one of the beagles and one of the beagles only and tell her husband that beagle was male. But that's not what was said. So your premise is gash.
From the blog post with the ""answer"
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?
Reduced to its essence, the problem is asking this: “There are two dogs. One of them is male. What is the probability that the other one is also male?
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.
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.
You can grumble all you like (and paraphase to suit - nowhere does he say "1 dog is male, whats the probability another dog is male. ') but nothing will cover up that your answer on page one was wrong and your are now looking for excuses 😉
As I said, in the original wording of the problem the phrase used was "the other one" which introduces the necessary uncertainty to allow for the 3rd possibility. I suspect you've read the solution but don't really understand how it relates to the question because everything you've said doesn't apply to the riddle as posed in the first post but does apply to the original phrasing of the riddle.
Although I would argue that even the correct solution is correct logically but wrong mathematically. If we label them as known and unknown and the first is the known male then "the other" has a 1/2 chance of being female. If the first is the known male then the "the other" has 1/2 chance of being male. If the first is the unknown then "the other" has a 1/1 chance of being male.
1/2*1/2*1/1= the probability of "the other" being male is 3/4. 1/3 doesn't account for the differential weighting of "the other" being the one we know 100% is male
Ah phrasing riddle and probabilities. Such fun. Oh how the brain and other people’s brain works .
I hope the buyer checks when he picks them up , as I had a workmate recently who got a cat called <span style="font-size: 0.8rem;">tinkerbell. </span>she recently discovered it’s actually a tom so had to change the name .. it’s now one confused cat
I suspect you’ve read the solution but don’t really understand how it relates to the question because everything you’ve said doesn’t apply to the riddle as posed in the first post but does apply to the original phrasing of the riddle.
Let you into a tiny secret - some of us havn't needed to look at the solution. Scary isn't it!
some of us havn’t needed to look at the solution. Scary isn’t it!
Not scary at all. If you think your solution is the answer to the riddle as posed is post 1 then it's just wrong. It is, however, the answer to the original riddle. Right answer, wrong question not at all uncommon.
A woman hides behind a black door. She can appear at the door with a deal or no deal. What are the odds she will appear with a deal?
From the question
What is the probability that the other one is a male?
So it does pretty much say what you say it doesnt say
nowhere does he say “1 dog is male, whats the probability another dog is male
Its a question written in a vague manner to conceal what he wants the question to be.
Not scary at all. If you think your solution is the answer to the riddle as posed is post 1 then it’s just wrong.
According to you. But you are wrong
I've got two oranges in my hands. One of them is rotten. What's the probability the other is also rotten?
The probability of a dog being male or famale is 0.5. It doesnt matter what the dog next to it is. Its a poorly worded question.
In your orange example you use "also" as does thecquestioner in what he says is the essence but not in the actual question
I’ve got two oranges in my hands. One of them is rotten. What’s the probability the other is also rotten?
Would depend on how both had been treated, its not fixed at conception by a 50:50 ratio of sperm like gender
The probability of a dog being male or famale is 0.5. It doesnt matter what the dog next to it is. Its a poorly worded question.
🙂
No one has ever been asked to consider just one dog at a time. The bather wasn't and the probability calculator wasn't.
If the word also troubles you, take it out. It makes no odds. Although I accept the other orange in my example is sat next to a manky orange so if it sits there too long whilst we procrastinate it doesn't matter and it'll be rotten too regardless.
So why add the word "also" to your orange example? The op's posted question was poorly (or well) worded by the questioner.
So why add the word “also” to your orange example?
Ok
I’ve got two oranges in my hands. One of them is rotten. What’s the probability the other is rotten?
Aside from cross contamination, what is the answer?
No one has ever been considered to think about just one dog at a time. The bather wasn’t
Alas, we’ll never know. She could have picked up the first dog by the scruff (phone cupped under chin whilst cursing her husband for calling her when he knows she’s bathing the bloody dogs) and seen its penis. No need to check the second dog then.
I’ve got two oranges in my hands. One of them is rotten. What’s the probability the other is rotten?
No idea, it depends on a huge number of other factors
According to you. But you are wrong
One of us clearly doesn't understand the difference between
"What is the probability that the other one is male"
And "what is the chance that there are two boys"
And I can assure you that it fundamentally changes both the logic and the math.
I've checked the probabilities and it 100% isn't me.
Alas, we’ll never know. She could have picked up the first dog by the scruff (phone cupped under chin whilst cursing her husband for calling her when he knows she’s bathing the bloody dogs) and saw its penis. No need to check the second dog then.
Agreed. As she was not asked to check if both were male she had enough information after the first inspection that she could stop fiddling with the dogs and still answer the question. But the dog she picked up was random. If she had been asked to check if 'Rover' was male then the question was is 'Fido' male I'd have some truck with the 50%ers. But she wasn't.
Have a think about this one then...
"I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"
"Your first impression is: what does Tuesday have to do with it?" says Gary, "And you might think that it doesn't. But in fact Tuesday has everything to do with it. And the actual answer to the problem is 13/27."
It's the same, but MOAR.
http://news.bbc.co.uk/1/hi/programmes/more_or_less/8735812.
WARNING: contains actual maths. It is correct, and extremely carefully worded. With these things (idealised probability puzzles) the wording is everything, it dictates the known, unknown and the answers.
Real word "what ifs" don't get a look in!
I’ve checked the probabilities and it 100% isn’t me.
I'd give that calculator of yours a bash - it seems to be on the wonk.
I’ve got two oranges in my hands. One of them is rotten. What’s the probability the other is rotten?
Aside from cross contamination, what is the answer?
Before I answer which one was closest to the bananas in the fruit bowl?
Before I answer which one was closest to the bananas in the fruit bowl?
They were arranged in an amusing two oranges and one banana configuration. The bowl however was on a treadmill. Going backwards. On a Tuesday.
Or to satisfy him up there...What is probability that both of the oranges I am holding are rotten? Because that is clearly a totally different answer.
They were arranged in an amusing two oranges and one banana configuration. The bowl however was on a treadmill. Going backwards. On a Tuesday.
Which way was the wind blowing the ethylene?
I understand that there are 4 possibilities before the wife is spoken to.
But why does her answer not rule out 2 options instead of one? Once she has looked at at least one dog, be it male or female then female-female is ruled out we all agree as she says that there is a boy, but surely male-female OR female-male is also ruled out because the sex of the dog she is looking at is known (even though we and the prospective purchaser don’t know it). Male-female AND female-male can no longer both be possibilities.
I understand that there are 4 possibilities before the wife is spoken to.
But why does her answer not rule out 2 options instead of one? Once she has looked at at least one dog, be it male or female then female-female is ruled out we all agree as she says that there is a boy, but surely male-female OR female-male is also ruled out because the sex of the dog she is looking at is known (even though we and the prospective purchaser don’t know it). Male-female AND female-male can no longer both be possibilities.
If you appreciate there were 4 possibilities before the phone call you are nearly there. So before the call there was a 25% chance both were males, 25% both females and 50% there was one of each. All the information gained over the phone allowed you to do is knock out one of the 4 options. So MF and FM are still on the table (along with MM).