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we know one is a male, this is M* so
M* M
M M*
M* F
F M*
50% chance
To present the same question in a different context:
You are a medieval king.
Your wife is pregnant with (non-identical) twins. You are desperate to have a male heir to continue your ruling line, and not start a bloody war.
(you know it is twins, and that they are fraternal, not identical)
The day before she gives birth, you calculate the change of you getting at least one heir is 75%, as there are 4 possibilties MM, MF, FM, FF. Which one of these is correct was decided 9 months ago, but is unknown.
If there is a male heir, the midwife is to send up a signal of white smoke. If there is no heir, black smoke. Ergo - white smoke 75%, black smoke 25%.
Immediately after the birth, you see white smoke. [you have the answer to your very specific question, which requires a Y/N answer. While there is more information, smoke signals cannot communicate this].
At this point after the smoke is white, there are now 3 possibilities. MM, MF, FM, where the first M or F represents the first born.
You are happy that you have an heir, but a new problem has presented itself:
At this point in time (after the smoke, and before you actually meet your children) what is the chance you have 2 boys who will be forever fighting over who is first born, and thus entitled to the throne?
Answer - one in three of the remaining legitimate possibilities, which have an equal probability of occurring, as it was decided months before.
There is no maths answer v common sense answer - the only non-real-world occurrence is that the pet shop owners wife who can easily find out the sex of both dogs, and then explain this in a full sentence through the wonders of telephone; instead chooses to correctly answer the exact, precise question asked with a yes/no one word answer, and venture no more information on the topic. Which is unlike any woman I have ever met.
We have one dog that is male, we’ll call him Ishmael, and we have one dog that is either, we’ll call them Leslie.
And by doing that you have made it a specific dog. That is information you do not have.
That is exactly why I originally explained this in terms of hands. Stating that Ishamael is the male is exactly the same mistake as saying the one in your left hand is male. You do not know that.
If you want to phrase it with names then we can do that.
But you don't know the gender of either Ismael or Leslie, you just know there is at least one is a male.
So either:
1) Ismael is male and Leslie is male
2) Ismael is male and Leslie is female
3) Ismael is female and Leslie is male
Surely this is only a question about one dog.
two dogs are advertised
one is revealed to be male.
the only question of 'chance' is whether the other one is male.
How do you know Leslie isn’t male and Ishmael is female? Why have you ruled that out as an option?
It doesn't matter, one of them is, one of them might be.
Note to self: must find a way to monetise this.
It doesn’t matter, one of them is, one of them might be.
Exactly,
So either:
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 happened to Ishmael?
Can we stick to M & F ffs 😆
"Call me Ismael." 😉
GrahamS - is this more fun than arguing with flat earthers?
GrahamS – is this more fun than arguing with flat earthers?
It is remarkably similar 😂
Your spreadsheet has GG as an outcome. We KNOW one is a boy.
we know one is a male, this is M* so
M* M
M M*
M* F
F M*
50% chance
*sigh*
*sigh*
Note to self: must find a way to monetise this.
100 door monty hall, with a small stake to win a reasonable prize? And hope everyone's a 50/50er. And doesn't watch the vids.
is this more fun than arguing with flat earthers?
oh and the latest Numberphile vid is indeed a map projection that demonstrates a flat earth 🙂
Yes, @ctk GG (or FF) is in the initial population.
It is a possible outcome at the start, before we receive the additional information.
As you can see, in that initial population of 1000 fairly assigned pairs, we have around 250 MM, 500 Mixed, 250 FF.
Once we find out that our pair is definitely not one of the FF pairs then we are left knowing that our pair comes from the remaining population of 250 MM and 500 Mixed pairs.
😂
ctk - Do you.not realise that by ascribing a * to one of them, you are assigning that a specific dog of the 2 is known to be male, thus making it a different problem to the OP.
It's already been noted a number of.times that if someone point to one of the 2 dogs and says that one is male, then the probability becomes 50%
The issue is that what you are presenting is not correct..
I can't believe this is still going, excellent 😀
When I read it first thing this morning I was in the 1/2 camp, but after the 2nd page and I think the sitting dog explanation it clicked and I got the 1/3.
Page 10, well done STW. Chances this is still going the same time tomorrow?
Peanut Butter M&Ms?
Would Revels not be better for this game?
I saw the light after a slow start. It's definitely 1/3
Say my wife is expecting twins. I tell the midwife that I will take both babies home if at least one of them is a boy.
I am in the waiting room, the midwife comes out to say I can take the babies home as at least one of them is a boy. One of three possible and equally likely scenarios has occurred
1) My wife has given birth to a boy then a girl. Outcome is I go home with 2 children of different sexes. This will happen 1/3 of the tim
2) My wife has given birth to a girl then a boy. Outcome is I go home with 2 children of different sexes. This will happen 1/3 of the time
3) My wife has given birth to a boy then another boy. Outcome is I go home with 2 children that are both boys. This will happen 1/3 of the time.
Importantly, outcome 1 and outcome 2 CANNOT be lumped into one. They are separate outcomes although on the face of it they appear the same.
Only 1/3 of the time will I be heading away with 2 boys.
For it to be 50/50 I would need to fix another fact to a particular child, such as the blond baby is a boy, what is the chance that both babies are boys. This insinuates that the OTHER child is not blond, hence the chance that the OTHER child is male or female is 50%. You can't do this with the OP because the problem does not give you enough info to pin down facts about a particular dog.
Hope this has cleared it up.
Probability 1 in 3
Chances 1 in 2
Probability is unable to realise that for the questioner m-f and f-m are one and the same.
this is somewhat marvellous. And I have to agree with The Cougar that the 52% think it is 50%
well done all
Do you not realise that by ascribing a * to one of them, you are assigning that a specific dog of the 2 is known to be male
Also it's like counting two ways to roll a double six: 6 6* or 6* 6
Probability 1 in 3
Chances 1 in 2
How exactly are you defining the difference between "Probability" and "Chances"??
Funnily enough we are going to the dog home for a look on Saturday. Dont like beagles ;-0
I genuinely cannot fathom the logic here. We have four options. We're then told that one of those options isn't valid. We're then left with two options. What?
I'm suddenly reminded of this.
Yeah that's probably a better way to think of it.
I've probably only got one other way of describing the problem and that's no.foubt been covered already in the thread but here goes.
Dog A and Dog B
FF
FM
MF
MM
If I say A is a male, you can eliminate 2 possibilities FF and FM leaving 2 equally likely options.
If I say at least 9ne of the dogs is a male then you can only eliminate 1 possibility FF leaving 3 equally likely options. This is the problem in the OP.
This works.if you run it with 3 sets of 2 dogs (AB,CD and EF). 12 options. Knowing one of each pair is M leaves 9 options with MM for all 3 being a third. If I said A, D and E were male then it leaves on 6 options with MM being a half.
How exactly are you defining the difference between “Probability” and “Chances”??
Well to calculate the chance of there being two male dogs when you already know that there is at least one male dog you can reduce m-f or f-m to one option but probability can't do that.
This boils down to whether MF and FM are the same or different but the key phrase here is the 'at least one' condition and the wife's positive response and I think the one-thirders are conveniently ignoring this....
Scenario 1 MM - only needs to check first dog before providing positive answer
Scenario 2 MF - only needs to check first dog before providing positive answer
Scenario 3 FM - needs to check SECOND dog before providing POSITIVE answer
Scenario 4 FF - needs to check second dog before providing negative answer
So, although there are three different scenarios where a positive answer is provide, the difference between scenarios 2 & 3 is actually irrelevant meaning there are only two outcomes - both males or one of each.
So the REAL scenarios are
Scenario 1 - MM
Scenario 2 - One of Each
Scenario 3 - FF
We know FF does not apply, so 50%...
Sorry to spoil the fun...
I imagine her with one dog out of the bath having just had its sex checked and one dog left in the bath that is yet to be checked. What I need to imagine is her pulling both dogs out of the bath at the same time, checking and confirming at least one is male and then putting them both back in 🙂
Probability 1 in 3
Chance 1 in 2
Probability 0.33333recurring
Chance 1 in 2
FTFY
Except the chance is 1 in 3 also...
when you already know that there is at least one male dog you can reduce m-f or f-m to one option
Sure, but, that one option is still twice as likely as the other one.
Scenario 1 MM – only needs to check first dog before providing positive answer
Scenario 2 MF – only needs to check first dog before providing positive answer
Scenario 3 FM – needs to check SECOND dog before providing POSITIVE answer
Scenario 4 FF – needs to check second dog before providing negative answer
Nowhere in the puzzle does it mention that she's checking dogs at all, you're adding / assuming information which isn't provided.
For all you know she happened to notice a few days ago that one had a willy and can't even remember now which one it was. In any case, even if she did know she doesn't then convey that information to the shopkeeper so it's lost knowledge at that point.
So the REAL scenarios are
Scenario 1 – MM
Scenario 2 – One of Each
Scenario 3 – FF
As above:
Scenario 1 – MM - 25% chance.
Scenario 2 – One of Each - 50% chance.
Scenario 3 – FF - 25% chance
Scenario three is reduced to 0% when we discover that they aren't both female, but the other two's ratio to each other does not and indeed cannot change.
It's one in three, I'm a professional mathematician and have been doing this sort of calculation for decades but most people are too simple-minded to understand it, sorry. The correct answers (there have been many) are correct.
Bah, we've had enough of experts.
The important thing to note is that the prior probability of boy and girl (in any order) is double the prior odds of two boys. If this isn't obvious you can check this yourself by tossing a pair of coins, repeatedly, and counting up how many times you get HH, HT, TH, and TT. Of the times that you got at least one H, in 1/3 of them you got HH, 1/3 was HT, and 1/3 was TH.
Nowhere in the puzzle does it mention that she’s checking dogs at all, you’re adding / assuming information which isn’t provided.
For all you know she happened to notice a few days ago that one had a willy and can’t even remember now which one it was. In any case, even if she did know she doesn’t then convey that information to the shopkeeper so it’s lost knowledge at that point.
Ok, point taken but you're obfuscating...
At no point in the OP was '''probability" mentioned either, and probability introduces a time component (ie the experiment is repeated). But for any one instance, this is a binary choice and the second dog is either male or female so for this one instance I don't agree with your assertion that "one of each" is twice as likely to occur as MM...
Saying "there are two possibilities, therefore they are equally likely" is a simple fallacy. Tomorrow, the sun may rise, or it may not. They are not equally likely.
you can reduce m-f or f-m to one option but probability can’t do that.
Riiiiight... so “Probability” is that pesky maths stuff but “Chance” is made up rules that match your gut intuition and gambler’s fallacy? 😃
You can merge two possible scenarios into one with probability, but you have to recognise that this increases the probability that it will happen.
As stated before, the probability of getting a mixed pair (either MF or FM) is twice that of a MM pair.
It’s one in three, I’m a professional mathematician and have been doing this sort of calculation for decades but most people are too simple-minded to understand it, sorry. The correct answers (there have been many) are correct.
Mathematician thinking this is a mathematical calculations riddle and making mistaken assumptions shock!!!
This is an English language riddle and understanding the very carefully crafted wording is the key.
(25+ year as a business analyst spent trying to get developers to do what the business needs them to do, not what developers assumes needs doing)
What's your favourite Revel?
No one likes the sub-Minstrels in there, do they?
and probability introduces a time component (ie the experiment is repeated)
How do you reach that conclusion? You roll a die, what's the probability that it's a 6? One experiment, not repeated, with a probability.
for any one instance, this is a binary choice and the second dog is either male or female so for this one instance I don’t agree with your assertion that “one of each” is twice as likely to occur as MM…
Then you'd be wrong. We've already established this - and the 50%ers have agreed - over multiple pages.
There is no "second dog," there is two dogs. They could be any permutation of MM, MF or FM. The only way this breaks is if you arbitrarily assign a definition to one specific dog, and nowhere in the puzzle is this suggested.
Mathematician thinking this is a mathematical calculations riddle and making mistaken assumptions shock!!!
Which assumptions are mistaken?
This is an English language riddle and understanding the very carefully crafted wording is the key.
I thought the consensus was that it was badly worded. My mistake.
A lot of these puzzles are imperfectly worded (Monte hall is the classic) but this one seemed pretty unambiguous to me. In suppose you could claim the setup was not the obvious one if you're desperate to do so but it is also a common maths puzzle (and challenging enough) when presented clearly.
I’m a professional mathematician and have been doing this sort of calculation for decades
Great so you can explain how:
Chances that both are boys
Chances that the other one is male and,
Chances that the other one is also male
Lead to vastly different mathemtical solutions. Since at some point in this thread the OP stated he/she/they/them changed the wording of the question.
Then we can move in to discussing something less controversial like how helmets do or don't prevent unnecessary cruelty to budgies.
12 pages? Good grief. Statistics is a well defined and exact discipline resting on hundreds of years of work. It's not a matter of opinion!
Can’t decide who is trolling, who still genuinely doesn’t get this and who just hasn’t read the previous posts. 😂
Since at some point in this thread the OP stated he/she/they/them changed the wording of the question.
I changed the wording from "what are the odds that the other is male" to "what are the odds that both are male" because I felt that as it stood it was (deliberately?) misleading. The rest of the puzzle is broadly as I found it.
I've been an ardent 1/3er from the start or this thread. But....I can see a sort of scenario or way of looking at this where you could conceive and 50% result as legitimate.
If we view this as we are witnessing an unfolding event where the wife could have said 'sorry no, they are both girls' but it just didn't play out that way the 1/3 result is obviously the correct one.
If we are however witnessing an engineered event where the wife will always answer yes so the final question can be asked where you ensure one dog is male when you set it up then the 50% result is the correct one.
The first scenario is to my mind at least the correct way to approach the problem. The second one is a bit daft. But I do now acknowledge it is a way of looking at the problem.
where you ensure one dog is male when you set it up then the 50% result is the correct one.
Only if you do that by specially selecting the initial population to give an equal amount of mixed-sex and all-male pairs.
But there is no suggestion of any shenanigans like that in the question.
Changed the question! Thats cheating.
you can check this yourself by tossing a pair of coins...
You're late - the other tossers are about 3 pages back!
😀
What’s your favourite Revel?
The peanut one. This is mainly due to the fact that an old school friend is allergic to them and when drunk would play Revel roulette. There was a 50% chance that 1/3 of the time he’d have breathing difficulties.
When are we starting on the original, unedited question then? Maybe that should be a separate thread...
The original is buried way back with a link to the formula but the 52% don't trust experts.
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?
I tend to agree with Cougar that the wording in that one is poorer as it doesn’t make it as clear which probability they are actually asking for.
For me it's easier to understand. 🤨
In changing the wording, the OP changed the question. The only way these riddles "trick" you into getting them wrong is the very careful wording. Changing the wording in this case makes the "right" solution wrong.
This riddle has been passed around the internet a lot and moved further and further from the original each time. 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"
It's likethee difference between what are the chances of ending up with 6 numbers in a lottery draw vs. the chances of ending up with your 6 numbers in a lottery draw.
In changing the wording, the OP changed the question.
It doesn't it just seems to confuse people but so does the original.
12 pages!! You guys are my ****ing heros!
Mathematician thinking this is a mathematical calculations riddle and making mistaken assumptions shock!!!
Which assumptions are mistaken?
That the population of this board is exclusively mathematicians? There could well be a significant number of Eng Lit students who study the story and do a different type of analysis, or 'people' people who apply Real Life experiences to their critical thinking....for example.
Lol: I'm seeing adverts from the Alzheimer's Association now...is that a co-incidence??
I'm always impressed by how much people can argue over the Monty Hall problem.
It's fairly simple to test it yourself if you don't believe the 'mathematical' solution.
I’m always impressed by how much people can argue over the Monty Hall problem.
I can see how people miss it. They concentrate on there just being 2 doors forgetting what information they have and can work out.
Argh! Why do I keep looking at this thread!
There could well be a significant number of Eng Lit students who study the story and do a different type of analysis, or ‘people’ people who apply Real Life experiences to their critical thinking….for example.
It’s a problem rooted in mathematics, it’s like saying we’ll agree to disagree about the answer to 1+2, there’s no ‘real life experience’ angle to it.
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”
But as far as I can see, neither Cougar’s OP text or the original stated here use that “also” phrase at all.
Cougar’s said: “What is the chance there are two boys?”
And this one said “What is the probability that the other one is a male?”
So are you complaining about a question phrasing that wasn’t put to you here on the grounds that it was stated badly elsewhere on the Internet??
Changing the wording in this case makes the “right” solution wrong.
The right answer in both of our cases as stated here is 1 in 3 or 0.33333333...
Wow. Just wow! Anyone who is still arguing against 1/3 is beyond hope. One page 1 sockpuppet did not just explain why it was 1/3, he essentially provided a mathematical proof - using the method of exhaustion. There is no further debate to be had. It is as definitely 1/3, as anything else you hold to be true.
Mathematician thinking this is a mathematical calculations riddle and making mistaken assumptions shock!!!
This is an English language riddle and understanding the very carefully crafted wording is the key.
(25+ year as a business analyst spent trying to get developers to do what the business needs them to do, not what developers assumes needs doing)
You maybe should have thought twice about posting this. It does not paint business analysts in a good light!
Speaking as a developer of 25+ years, it paints Business Analysts in exactly the light I expect. 😂
Maybe leave the number stuff to the engineers?
boys != male puppies
FFS, 12 pages. Very impressed.
12 pages? Good grief. Statistics is a well defined and exact discipline resting on hundreds of years of work. It’s not a matter of opinion!
What's that old quote Moly? Something something damned lies and statistics?
Statistics can say exactly what you want them to depending on how you select your data, no wonder this is a 12 pager! If you wanted it to be concise you would use facts instead 😉
Evening once more.
Interesting that all the 1/3ers have ignored the point I made about how you use the new information, with the exception of convert who is nearly there but too entrenched to admit he is wrong even though he might understand it.
This isn't a maths problem, the maths is simple. It's a philosophical problem about how you use information.
If you check the sex of one dog, and then check the sex of the other, then 1/3 is the correct answer.
Unfortunately, this does not describe the problem.
One dog is male, one dog is either, and it doesn't matter which one is which.
It is interesting to see how the different "personality types" manage or fail to deal with this idea, though I am surprised so many are struggling with (or plain ignoring) it. 🙂
depending on how you select your data
Getting closer!
As an example of a glaring and easily understood nature, which demonstrates what happens when you make seemingly inconsequential changes without grasping that they change the fundamental underlying assumptions of the problem. It isn't about math or stats. It is logic and language. You can put whatever numbers you like into a spreadsheet and prove your answer but if you've read the question wrong it won't help in the least.
@sbob: I didn’t ignore it. I tried creating a new model from the position of knowing that it is not a female-female pair, as you suggested, and I got the same 1/3 result.
You also said try calling them Ishmael and Leslie. I responded to that but you have cunningly ignored it.
I wonder what the overlap is between people that think it is 50:50 and people that think the plane on the conveyor can’t fly?
If you check the sex of one dog, and then check the sex of the other, then 1/3 is the correct answer.
Getting closer!