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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
It’s maths probability problem
Why’s it written in words and not numbers then? Stick to your own ways mathematicians!
One is basically “We have determined Dog A is male; what are the odds that Dog B is male?” Answer: 1/2.
If that is your interpretation then you have misinterpreted the problem.
TIME FOR EXPERIMENTATION!!!
Take 2 coins ("two Beagle puppies")
Tails is male, heads is female.
Toss both coins say 100 times, recording your results each time.
Strike out all results where you get 2 heads/females ("asks her if there's at least one boy. She says yes")
Work out the proportion of double tails/males versus the mixed results (heads/tails or tails/heads)
"What is the chance there are two boys?" - you have your answer.
Has anyone asked the dogs as what they identify as?
“We have determined Dog A is male; what are the odds that Dog B is male?” Answer: 1/2.
That isn't quite right though is it? Dogs A and B are selected from a pool of two dogs so dog A becomes dog A only if it is male. If it isn't then you effectively choose dog B to be dog A. That means dog B is less likely to be male as it is either the rejected female dog or a 50/50 random dog. You still get 1/3 for dog B being male. Sorry i probably haven't written that very clearly.
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
This.
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.
This is correct, and what we've all been saying for 15 pages. However, nowhere in the puzzle does it suggest that we have identified one specific dog, at all. The puzzle asks "is there at least one boy?"
Any solution that starts with "take one dog..." is inherently wrong because it's assuming knowledge that we are not given. Any solution that starts with "the wife checks the first dog and..." is inherently wrong because it's assuming knowledge that we are not given. 50:50 is the totally correct answer to an entirely different question.
This has been explained in lots of different ways and at this point sbob and others have just chosen to ignore the fact that they are wrong. There is only one answer and that is 1/3.
The fact that those saying 1/2 can't demonstrate it with any logic outside of "the wording" or "pick up dog a, then dog b" speaks volumes, especially since it's already been stated a number of times, that any interpretation where the male dog is known leads to 1/2 probability.
The questions isn't poorly worded, it's very specifically worded.
Edit: Urrrghhh those formatting marks 🙁
However, nowhere in the puzzle does it suggest that we have identified one specific dog, at all.
And yet that is precisely what you have to do to arrive at the four freedoms, err outcomes. If you don't do that then you can't achieve M/F and F/M as the separate outcomes you need to reach the 1/3 conclusion.
Otherwise you return to the situation where either of the dogs is male, the other might be.
Right sbob, but the question takes place before we've checked which is male. We only know 1 is, with the information provided by a 3rd party.
As it could be either or both, we have to account for all outcomes.
This has been explained in lots of different ways and at this point sbob and others have just chosen to ignore the fact that they are wrong. There is only one answer and that is 1/3.
It has been explained in exactly the same way just with added levels of obfuscation. Stating someone is wrong is not proof that they are. I repeated several times that I fully understand the 1/3 maths but it is down to the interpretation which I have explained.
We only know 1 is, with the information provided by a 3rd party.
We know one is, but we also know the other might be.
The questions isn’t poorly worded, it’s very specifically worded.
I asked ages ago how those suggesting that it's badly worded would reword it to make it clearer, but oddly no-one answered. As I said, I tried myself to tidy up the wording before posting as I felt the version I'd started with was (deliberately?) misleading.
I think Drac sums it up well.
Not yet Drac, just five more pages.
Not yet Drac, just five more pages.
I've only two and a half hours til work, make 'em count.
It's still going? Absolutely glorious 😀
Top work Cougar 😆
Top work Cougar
mattoutandabout would be proud!
I’ve only two and a half hours til work, make ’em count.
Didn't stop you last night.
I asked ages ago how those suggesting that it’s badly worded would reword it to make it clearer
I'm not suggesting it was badly worded and it's clear you did tidy up the wording from the WIki wording. However, if you wanted to make it clearer you could have explicitly stated that both Beagles were placed back in a pen together and were mixed up with no clue as to which Beagle had been identified as the Male.
But you'd *never* have got to 15 pages that way.
Ok, so in the interest of clarity: I have just tossed 2 coins 50 times.
The results are:
HH: 17
HT: 18
TT: 15
I mean what are the chances of that?
Wait, I've got a solution which satisfies both camps.
Assuming for the sake of argument that @sbob's approach is valid, he's asserting (paraphrasing so correct me if I'm wrong) "we know one dog is male, therefore the other is male or female, so the likelihood of the other being male is 50:50 / 1 in 2." Now.
we know one dog is male, therefore the other is male or female
This bit seems pretty inescapable, yeah? But is it logical to then conclude,
so the likelihood of of the other being male is 50:50 / 1 in 2.
❓
We've taken this as a valid conclusion for 15 pages, and it turns out, no, it's an erroneous logical leap.
We know the other is male or female, sure. But we also know that the probability of pairings are not evenly distributed. From Graham's spreadsheet we can see demonstrably that the likelihood of a M/F pairing is twice as likely as a M/M pairing.
So even using sbob's logic, the answer is "we know one dog is male, therefore the other is male or female, with the given distribution the likelihood of the other being male is 33:67 / 1 in 3."
*mic drop*
Didn’t stop you last night.
Boo to you, fun-sponge.