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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).
But FM=MF in this case as it doesn’t matter which of those combos occur.
Another vote for this being the Monty Hall problem with some Chinese whispers added which inadvertently change it to something else.
Not Monty Hall. There are no doors you have to choose from. You get what is behind both doors.
You get what is behind both doors.
You do. Only snag for you 50%ers is that all you know is that there is a male beagle behind one of the doors. Neither door has yet been opened.
if i back 2 football teams to get into the next round of the FA Cup,
the outcomes are WW, WL, LL (i guess others would say WW, WL, LW, LL)
lets say the early game i get the result and win, as result one is known then its 50/50 on result two to win overall..
hence a bookie may be willing to offer a cashout
it all depends if you see the two items as related. when you know the outcome of one result in a pair, then the next result is always 50/50, but overall the probability is not 50/50..
ah, im back nice and refreshed after a good nights sleep and ready to fight the good fight in the name of common sense....... which may be the problem here, people arent using good old common sense and reading the question for what it is. RTFQ!
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.
......is all that matters here. youre complicating matters by comparing this question to opening doors, tossing coins.... why put yourself through the pain?
RTFQ! nowhere does it say the woman replied that yes one is male but im not telling you which yet youve got to work out the likelihood of only dog B being male.
also the question doesnt say 'according to the laws of maffurmatics give the right answer....'. it just says......
A man sees a sign in a window advertising two Beagle puppies for sale. He goes in and tells the shopkeeper he will only take the puppies if there’s at least one boy.
The shopkeeper phones his wife who is bathing the dogs and asks her if there’s at least one boy. She says yes.
What is the chance there are two boys?
theres at least one boy, doesnt matter if its A or B, whether she looked at one dog or two to get there, she could have said yes theyre both boys but didnt, she just said theres at least one boy. so options left are theyre both boys, or theres one boy and one girl.
again, doesnt matter if the BG combo is A (male) and B (female) or t'other way round. MF or FM, doesnt matter one jot according to how the question is worded. those who dont say 50% are adding or taking away info that isnt given or required. RTFQ!
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?
Because observation does not change the likelihood.
There are four equally likely permutations before the wife is spoken to. This doesn't magically change with the addition of extra information. We are told that at least one is male.
If both are male, is at least one of them male? Yes.
If one is male and the other female, is at least one of them male? Yes.
If one is female and the other male, is at least one of them male? Yes.
If both are female, is at least one of them male? No.
I applaud your passion sadexpunk - but you are still wrong 🙂
So, How many were Heagles and how many were Sheagles?
she just said theres at least one boy. so options left are theyre both boys, or theres one boy and one girl.
That is correct. However, what you're missing / ignoring is that the probability of those two options are not equal. It's twice as likely to be the latter than the former.
those who dont say 50% are adding or taking away info that isnt given or required.
Quite the opposite. Those who those who do say 50% are adding or taking away info that isn't given or required. They're prescribing "one is male" to an individual dog and then going "well, the other one must be male or female then." You can't do that, it ignores the notion that the one that is male might be the other one.
If nothing else at least this thread explains Brexit
In a weird way making the question a tiny bit more complicated might help some of you to understand...
There are now three puppies being bathed. The wife tells her husband that at least one of the puppies is male. Do the 50%ers still think the chance of all 3 being male is 50%?
Take is one stage further (stupider). There are 100 puppies in the bath. The wife tells her husband at least one of the puppies is male. Do the 50%ers still think the chance of all 100 being male is 50%?
If you don't, explain why not, give the correct answer and show your workings (on the 3 puppies scenario as the 100 puppies version might take a while) It's the same principle.
If nothing else at least this thread explains Brexit
Indeed and not (necessarily) in a negative way. Two groups facing the same set of facts and both absolutely convinced they know the answer based on what is in front of them. The fact that one of the two groups would probably fail their GCSE paper if they took it tomorrow is neither here or there 😉
That is correct. However, what you’re missing / ignoring is that the probability of those two options are not equal. It’s twice as likely to be the latter than the former.
herein maybe lies the crux of the issue if we can bash this out. i say its not twice as likely, its the same. and sorry convert, much as im willing to look at other ways around this, i cant even think about 3 or 100 dogs as thats not what we're faced with. im only interested in this one question and how its worded 🙂
sorry convert, much as im willing to look at other ways around this, i cant even think about 3 or 100 dogs as thats not what we’re faced with. im only interested in this one question and how its worded
Promise it will help. Get the answer to the 3 dog question right, then explain why you are not using the same method to the 2 dogs question. It'll be cathartic.
@convert can you understand why people with one result in hand then assume its 50/50 on the second bet..
google "tossing a coin twice in a row odds" may help
You know from experience that if you flip a coin twice, sometimes you get tails twice in a row. That is because each time you flip the coin, the odds remain 1/2; the two flips are independent of each other. The odds of getting tails twice in a row are 1/2 * 1/2 = 1/4. So 25% of the time you'll get heads twice in a row.
but as the majority of 50/50 comments state, you know the result of one hence, the next result is independent
hence 50/50 you can only have heads or tails.., the probability you get it is 1/4
if i was in the pub i think i'd go for 2 heads in 3 tossers, better odds
herein maybe lies the crux of the issue if we can bash this out. i say its not twice as likely, its the same.
Try this: Before we know anything other than there being two dogs the probabilities are FF =1/4, MF = 1/2, MM = 1/4. MF is twice as likely as MM. Do you agree with that?
Now, probably the tricky bit. The only thing we are told is that "there is at least one boy" and with that information all we can do is exclude option 1, it isn't FF. MF is still twice as likely as MM so the odds are now MF = 2/3, MM = 1/3
i can see your way of thinking cougar (or i think i can anyway), youre thinking we've still got two dogs to play with, whereas im saying we've got one. as soon as the wife says at least ones male, then its gone, out of the running, its deceased, it is no more, its a dead dog.
another way of wording it......whats the chances of the other one now being the same as that male one 😉
herein maybe lies the crux of the issue if we can bash this out. i say its not twice as likely, its the same.
If the wife was busy and didn't answer the phone do you agree that at that point the chance of one male and one female was twice as likely as both male?
Try this: Before we know anything other than there being two dogs the probabilities are FF =1/4, MF = 1/2, MM = 1/4. MF is twice as likely as MM. Do you agree with that?
no i dont. options are FF, MM, or MF/FM. 3 options.
convert, ill try 🙂
but as the majority of 50/50 comments state, you know the result of one hence, the next result is independent
No you don't. As I've said previously if the dogs were called Rover and Fido and the question as was if Rover was male I would agree that the answer to the question is Fido male is independent and indeed 50/50. But we never names the dogs. We didn't gender test them in a defined order. It really matters.
No you don’t.
you do. the result is 'one is male', doesnt matter whether its rover, fido or noname. ones male. chances left are 2 males or male/female combo. the sex of an individual dog, that dog there doesnt matter.
convert, ill try
I'm glad. But hang on....
no i dont. options are FF, MM, or MF/FM. 3 options.
We've got some work to do first on this bit.
I've got some work to do; can you go play with a couple of coins for a bit and see if you still believe this and I'll get back to you.
can you go play with a couple of coins for a bit and see if you still believe this
no, cos the coins may be different to the dogs, so im not going to confuddle my little head any more 🙂
no i dont. options are FF, MM, or MF/FM. 3 options.
Ok, I think I see where the problem is. Do you also think that your chances of winning the lottery are 50/50? You either win or you don't, 2 options 🙂
This thread is great. I voted to stay in the EU and understand how the thought process and probability of 1/3 answer works. Yet I still think 50/50 is the correct answer. Any other answer just seems daft when we already know ones a bloke.
Where does this leave me?
Does the bloke have his Beagles?
Are they to be kept as pets or used as working dogs?
Do the dogs know what gender they are and is one more likely to have a career as a nurse?
Yours sincerely,
Confused of Macclesfield.
The shopkeeper phones his wife who is bathing the dogs and asks her if there’s at least one boy. She says yes.
What is the chance there are two boys?
We know one dog is male. It doesn't matter which one, we are only concerned with the sex of the other dog which can only be male or female.
Ok, I think I see where the problem is. Do you also think that your chances of winning the lottery are 50/50? You either win or you don’t, 2 options 🙂
poor, very poor. there are 14,000,000 other people with a ticket, why would i think its 50/50? must try harder. again, RTFQ and see it for what it is.
Are any of the dogs pink?
We know one dog is male. It doesn’t matter which one, we are only concerned with the sex of the other dog which can only be male or female.
What is even worse is the fact that theoretical beagle buying man doesn’t give a shit and we’re at six pages 😀
Once he heard the words “Yep, ones a boy” he was done and happy and couldn’t care less about the other dogs gender.
MF is different from FM because the gender of one dog is independent of the gender of the other so there are four options available (MM, MF, FM, FF) but we are given an extra bit of information that one dog is male so we can discount the FF option. This means that both dogs being male is one option of three.
If I toss two coins one in each hand I have four possible outcomes: both heads; LH heads, RH tails; LH tails, RH heads; both tails. The probabilities of all four outcomes is 1/4. The probability of getting one coin heads and one tails is 2/4. If I toss the coins sequentially and it comes out heads that does not change those probabilities so the odds of the second coin being heads is 50% because it's an independent event but the odds of both being heads is 1/3.
I got halfway through the first page and decided some people have way too much time on their hands!
Now, probably the tricky bit. The only thing we are told is that “there is at least one boy” and with that information all we can do is exclude option 1, it isn’t FF. MF is still twice as likely as MM so the odds are now MF = 2/3, MM = 1/3
It's 50/50.
The position of the male puppy doesn't matter because whichever position it is in, it exludes either MF or FM. Your MF at 50% overall likelihood doesn't hold water.
You can't say that both of those are still valid options just because you don't know the position. You can only say one of them is valid, but we don't know which. Either way, you are back to two options. 50/50. Anything else is a distraction.
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.
It's a very carefully worded question, which is why the correct answer is not the "obvious" one.
There are two dogs and you know nothing specific about either one. The only thing you know it's that both of them are not female. So the unknown dogs could be MM, MF or FM. That's three options, only one of which is the outcome you want.
The probability of a random, new dog being born male is 0.5, but that's not what is being asked here. The two dogs already exist, and all you know it's that they are not both female.
So the unknown dogs could be MM, MF or FM.
no they cant, MF is the same as FM. which dog is which doesnt matter. crack this one and we'll all agree 😀
Yay! The Boy/Girl Paradox. Sorry to be late to the party.
I posted this to the old old forum many many years ago and it went for twenty odd pages.
The correct answer is 1/3.
The easiest approach for people that don't get it is to do a spreadsheet and prove it empirically.
Hang on.. I'll knock on up...
If the first dog being checked was female what is the probability of both dogs being male?
You'll answer, correctly, zero.
If we are only concerned with the gender of the second dog, as stated above, then the answer apparently is 50%!
@sadexpunk - look at my coins example which is the same problem.
The 3 possible outcomes of MM, MF, FM makes perfect sense though the way the question is worded means MF and FM is the same as one they both mean only one is male. Its a good one that makes a lot of people over think a question. We know one is male so the question is simply what are the odds of the other one being male. 50/50.
I just asked my wife....what is the probability we will be getting a divorce?
You can’t say that both of those are still valid options just because you don’t know the position. You can only say one of them is valid, but we don’t know which. Either way, you are back to two options. 50/50. Anything else is a distraction.
But both of those options are still valid. I know SP doesn't like it but the coin toss analogy works well here. Toss two coins. HH 1/4, HT 1/2, TT 1/4. Now discount any results where you don't have at least one head (ie one or more of them is a head, so all you can discount is TT) the results will now be HT 2/3, HH 1/3. Same for the dogs. You can try it with the coins, should only take 20 or so tosses to start seeing a trend
@mjsmke - the probability of the second dog being male is 50% but that isn't what is being asked. MF & FM are valid and separate probabilities so have to be taken in to account since we don't know which of the two dogs was checked for gender.
herein maybe lies the crux of the issue if we can bash this out. i say its not twice as likely, its the same.
But... well, it's not. I don't know how else to explain this.
Take the second bit of the question out of the equation for a moment. You have two dogs at random. The likelihood that they're the same gender is the same as the likelihood that they're different gender, yes? 50:50, they're either the same of different.
Now we remove one of those "same gender" options, we're told that they aren't both girls. You're arguing that the likelihood of them both being either the same gender or different is still 50:50? How is that possible?
another way of wording it……whats the chances of the other one now being the same as that male one
That's not another way of wording it, it's a different question entirely. You're arbitrarily singling out a specific dog and then asking questions of the other one. What if it is, in fact, the other dog which has been identified as male? You're completely ignoring this possibility, which is why your maths is wrong.
You can try it with the coins, should only take 20 or so tosses to start seeing a trend
Coin tosses are not a valid analogy, we are looking at a single pair of dogs and we know that one of them is male.
If the question posed was asking what the likelihood of a second dog being male in any given family randomly chosen from a dataset where we knew that at least one puppy was male then that would be valid. In this case, we are not. We are looking at a single data point, and we know that a randomly slected puppy is male.
Just had a thought - could we tweet this to Donald Trump? It'd keep him busy for years!!
And as others have said, the coins is a perfect analogy. It's the same question. You've got a pair of things that can be one thing or another and are asked to discount one permutation.
Take two coins and flip them repeatedly. Record the results of two heads, two tails, or one of each. Now, cross out any results for whom the answer to "is there at least one head?" is "no". Would you expect to see a similar tally of two-heads to one-of-each? If your answer is "yes" I strongly suggest that you actually try it as an exercise.
Coin tosses are not a valid analogy, we are looking at a single pair of dogs and we know that one of them is male.
Coin tosses are a valid analogy, we are looking at a single pair of coins and we know that one of them is heads.
Coin tosses are a valid analogy, we are looking at a single pair of coins and we know that one of them is heads.
And you are now suggesting that the probability of throwing another head is 1/3?
Okay here's my spreadsheet...
https://docs.google.com/spreadsheets/d/1T7BqW-IdB-5xZp3CE0cql6qaWHLtLGSFCriMCpoYRsQ/edit?usp=sharing
It generates 1000 scenarios of two dogs, where each dog has a random 50:50 chance of being male or female.
You can see for yourself that empirically, in actual results, the probability of both dogs being male consistently comes out at around 1/3
No mathematical trickery involved.
A man sees a sign in a window advertising two recently-tossed coins mounted in a display case. He goes in and tells the shopkeeper he will only take the coins if there’s at least one showing heads.
The shopkeeper phones his wife who is washing the case and asks her if there’s at least one facing heads-up. She says yes.
What is the chance there are two heads-up coins?
That’s not another way of wording it, it’s a different question entirely. You’re arbitrarily singling out a specific dog and then asking questions of the other one. What if it is, in fact, the other dog which has been identified as male?
if it was the other dog that had been identified as male then we'd have the other dog that would be male or female.
I know SP doesn’t like it but the coin toss analogy works well here. Toss two coins. HH 1/4, HT 1/2, TT 1/4. Now discount any results where you don’t have at least one head (ie one or more of them is a head, so all you can discount is TT) the results will now be HT 2/3, HH 1/3.
that just messes my head up trying to think that through, so im sticking to what we've been told about these 2 dogs. ones male, whats the chances of them both being male then. 50/50
And you are now suggesting that the probability of throwing another head is 1/3?
Why are you throwing one of them again? They're already tossed, you're then simply observing the results.
Observing the coins doesn't change the probability, putting one arbitrarily aside and re-tossing the second demonstrably does.
LOOK AT THE SPREADSHEET.
It will all become clear.
Hopefully.
Is it any wonder that bookies always win (sigh)
It generates 1000 scenarios of two dogs, where each dog has a random 50:50 chance of being male or female.
You can see for yourself that empirically, in actual results, the probability of both dogs being male consistently comes out at around 1/3
nice spreadsheet, but we've got a bit more information now, we're told that one of the dogs is male, thats a certainty. 100% male. so whats the chances of the second dog being male and hence having 2 male dogs? 50/50.
i can see what youre doing/saying, but all your maths is from a point where we know nowt about them poor wet pooches, we now know that at least one is male. you dont need a spreadsheet for that.
LOOK AT THE SPREADSHEET.
That's got my geek gene a purring.
we’ve got a bit more information now,
Yes but that information only lets you narrow down which scenario you are in. It doesn't change the original odds.
The original odds are that if you do this 1000 times you'll see "both boys" about 250 times and "mixed or both girls" about 750 times. Correct?
The information that at least one is a boy means you can ditch the "both girls" scenarios and you now know you are either in one of the 250 scenarios where they are both boys or one of the 500 scenarios where they are mixed.
Do the 50%ers still think the chance of all 3 being male is 50%?
Well I dont. But as I said my problem was with the wording, which was imo different from what he wrote in the explanation of why the answer wasnt 0.5.
It might make a little more sense if you think about the odds improving, not getting worse.
Before you have any information there is a 1/4 chance that they are both boys.
Once you know that at least one is a boy then you know there is a 1/3 chance they are both boys.
Yes but that information only lets you narrow down which scenario you are in. It doesn’t change the original odds.
but why do you need to keep the original odds the same? the odds have now changed, as we now have more info.
The original odds are that if you do this 1000 times you’ll see “both boys” about 250 times and “mixed or both girls” about 750 times. Correct?
yes.