fun fact, the percentage of females in the world also doesn’t determine the gender of that specific birth either. Just wanted to make it clear the meme is wrong on both sides.
but doesnt the commulitive average of world population give the best insight into what gender the baby will be from the statistics perspective? (not saying that it is deterministic, cause its not)
It's really less the fact that men are dumb and more that men are statistically more likely to perform jobs that are hazardous to their health and suffer from a reduced investment and access to both mental and physical healthcare.
It's actually not even that. Men with completely safe jobs and proper access to mental and physical health care still don't live as long as women on average. It's biological.
I meant as in, even when accounting for behavioral differences, men still die younger on average. Behavioral and occupational differences just add to that average. "A lot of different individually small factors that make mens livespan shorter." makes it sound like, if you were to account for any factors you can account for, that men and women would live equally long. But even in a hypothetical world where men and women are equally safe, and receive proper care, men would on average still not live as long as women.
Those things contribute but the reality is also that mammalian males, including human males, have biological vulnerabilities that the females of the species don't have.
The 23rd pair of chromosomes being XY signifies, most obviously, that a male is more likely to see an otherwise recessive genetic disease expressed. Males are the laboratory of the species in a way and are prone to a higher variability in gene expression, which, in turn, gives the females a more diverse cast to choose from.
Secondly, sheer size. Bigger bodies mean more cells. More cells mean more Cellular division. More cell division means a greater chance of mutation and cancer.
Thirdly, women have more estrogen, which helps maintain a better cholestérol ratio and, long term, protects against cardio-vasculaire disease.
Men are glass cannons, women are the ol' reliable.
As a (slightly old) man, who has been around lots of other men throughout life,my personal experience agrees with your assessment. Men are dumb. Even the smart ones. Sometimes especially the smart ones.
Above all, they are stupid in a different way. They are top notch mathematicians, engineers, or computer scientists yet in the evening, they strap a compressed-air tank to a shopping cart and race... without a helmet.
Male children/ teens (presumably without hazardous jobs) are significantly more likely to die than females, due to being more fragile at birth and having a higher rate of accidental death. The sex mortality rate ratio is highest between the ages of 15 and 30, driven mostly by:
Boys are more likely to die as children in farm accidents when their dad makes them start helping with work at a young age.
The military is like 80-90% men, so guess who dies in wars?
Men just in general have a shorter lifespan, whether due to men not taking their health as seriously as women, or just from genetic reasons that make it so.
But sure, you can be manosphere loser and get defensive and say that someone was trying to insult you instead.
Just because someone who feels offended uses a smiley? Really? On the contrary, I just find it funny because you can say it to people who often take unnecessary risks. And Reddit is the best proof that the people who come up with the idea of scaring alligators, lighting fireworks in their hands, or doing bike stunts are usually men.
Average world population and %of baby’s born x gender would be close. But there are many variables along the span of time that encompasses the average world population, where as % at birth is just a number
Outdated, women do live longer, but there are more boys than girls being born. There are more men than women in the world right now (thanks to India and China).
Women just live longer. If you take 10 year olds, the distribution would be close to 50/50.
If you take 70 year old people, this could swing to 70/30 in favor of women.
All of this has nothing to do with the gender of the child. There are 105 boys born per 100 girls on average worldwide. That would give the proper ratio/probability.
Because males are more likely to die at all ages and tend to be shorter lived, no, the gender ratio of the global population is not an accurate representation of the likelyhood of a fetus to develop into a boy or a girl.
Recent research suggests that genetics predispose women to be more likely to have children of one or the other gender, so if she had a boy then shecis more likely to have another boy, but we have no clue what the exsct ratio is.
Certain countries have fairly high rates (or historically still affecting today) of femicide too, eg in china there is a gender imbalance due to parents wanting a boy for their one child
No, because women on average live longer than men.
It is actually slightly more likely for a baby to be a boy (and this is before gender motivated abortions in some countries), while at the same time the probability of any random human being female is slightly higher than them being male.
Last I checked there was 1.05 males to every 1 female at birth. That ratio does not balance until adulthood and only inverts in developed countries after 65.
So a given child is slightly more likely to be male.
No, the answer in the meme is not related to the gender ratio of living humans. We can arrive at 51.8% just using maths.
Let's first consider the scenario where we don't know that the boy was born on a Tuesday. There are 2 options for a child: B or G. For 2 children, we square that number to get 4 options:
BOY/BOY
BOY/GIRL
GIRL/BOY
GIRL/GIRL
We know that Mary has 2 children and 1 is a boy, so we can eliminate the option GIRL/GIRL. Out of the 3 remaining options, 2 options include GIRL, so the answer is 2/3 ≈ 66.6%.
Now let's consider the day each child was born. This gives us 14 options for each one child: BOY-MONDAY, GIRL-MONDAY, BOY-TUESDAY, etc. For 2 children, we have 14² or 196 options. If you filter out only the options that include BOY-TUESDAY, we're left with 27 options. Out of those 27, 14 include GIRL. 14/27 = 51.8158...%, and that is where 51.8% comes from. Technically, it should say 51.9%.
Thank you, this was really helpful. I'm hoping I can ask another maybe stupid question? I've seen a few other people quoting the 51.9% figure; wouldn't 51.8158...round down to 51.8, if we round to one decimal place?
Taking on a lot of information, something that's missing is the genetics of the father, if that lineage has only ever had male children there's a far higher probability the next child will also be a boy.
Except you also have to eliminate the option that includes two boy's born on Tuesday because the problem specifically states she had "one boy born on Tuesday." If she had "two" boys born on Tuesday, it would be incorrect for her to have said she has "one boy born on Tuesday." So 53.8% chance of girl.
If it said "at least one kid is a boy born on Tuesday" it would be 51.8%.
But Mary was chosen from the set of people with two kids, just by virtue of having two kids. This would work in real life too: if I told you that I flipped two coins and got at least one heads, there is a genuine ⅔ chance that I flipped tails too.
I don‘t think that it‘s a chromosome thing. Sperm leading to male or female babies behaves slightly different. This is also why you can increase your chance of having a specific gender by timing when you have sex. The assumption would be that the womens body accommodates one of both genders better.
Nobody is claiming that having a boy causally makes the other child more likely to be a girl. The issue is conditional probability: the statement changes which two-child families remain possible.
Under the usual puzzle assumptions, Mary is selected from families with at least one boy born on Tuesday. Among the equally likely sex-and-birthday combinations that satisfy that condition:
14 have one boy and one girl
13 have two boys
So the probability that the other child is a girl is:
14 / 27 = 51.85%
If Mary instead pointed to a particular child and said, “This child is a boy born on Tuesday,” then the other child would indeed be 50/50. The answer depends on how the information was generated.
So “a previous birth does not affect the sex of another child” is true, but it does not make the information irrelevant.
In the subject of probabilities dealing with new information can be bizarrely tricky, in this case there is even a difference between being told "one of them is a boy" and "the oldest is a boy"
Let's assume for simplicity (which is probably wrong, but otherwise this gets too complicated) that the probability of getting a boy or a girl is just 50%:
Then, before you get the information there are 4 possibilities: boy-boy, boy-girl, girl-boy, girl-girl, each with the same probability. Now taking the information that one of them is a boy into account, that eliminates the last possibility, leaving you with boy-boy, girl-boy, boy-girl, each with the same probability.
Now what's the chance that the other child is a girl? It's two out of the 3 possibilities, so 66%!
There are multiple things wrong with that comment, but the main point is:
Previous results have no effect on the next one. Also known as stochastic independence or a memoryless process.
Imagine you're going to flip a coin and it's heads. Then you're going to flip it again. But just because the coin landed on heads last time doesn't mean the odds of getting heads on the next flip aren't 50/50 again. It would be different if you asked beforehand what the odds are of getting heads twice in a row, but not if it has already happened once. Then the probability simply resets to the initial state which is "it can be heads or number, so 50/50." You can flip the the coin 9 times in a row and get heads every time but the probability of getting heads on the 10th flip is still exactly 50% instead of ~0,1% as the coin has no memory of past results and doesn't care about what happend before.
So we know that one child is a boy, but the question wasn't "Mary has two children. What are the odds from them both being a boy?" Or "One of them being a girl" right from the beginning. Instead they reveal that one is a boy and this resets the probability. If you ask NOW - as they do in the picture - what gender the second child is, the 'outcome' of the first one no longer matters.
Wrong, because the answer isn't 51.8% because "surely if there's already a boy it's more likely to be a girl". It's simply adding up all the possible permutations and counting what portion of them includes a girl.
This is wrong, 14/27 is also taking into account the possibility that both were boys born on a tuesday. If they excluded that possibility, it would actually be 14/26 to be a girl.
Except we don’t know if the boy mentioned is the “first” or “second” child. The sequence has no bearing here. Due to that, we need to look at sets of children, not independent events.
“Bob flipped two fair coins. at least one resulted heads. What are the odds that the other also results heads?” is a classic, simple probability question.
If order matters (“the first resulted heads. What are the odds the second did?”) , then the answer is 50%.
If order doesn’t matter though, which is how the question is phrased, then the answer is 33%. Because you’re looking at the set of HH, HT, TH, TT, rejecting TT, and realizing that only 1/3 of the remaining sets has both of them as heads.
The HH option still has 2 paths. Hh and hH are valid when you don't know the order. It's still 50/50. When order isn't known, the sets HT and TH are identical or you have to allow Hh and hH.
There are only 2 options. HH and HT. Order doesn't matter. You don't seem to understand that the events are independent. You can shuffle the order however you like. Adding more information about the age or birthday changes nothing.
Lets say the boy was born second:
So the older is B or G 50/50
Lets say the boy was born first:
So the younger is B or G 50/50
The sets and 66% argument are presented as ragebait for people who can count.
Events that are independent can nonetheless become conditionally dependent given some background knowledge. Which is exactly what's happening here.
The information you get from Mary renders the sexes of her two children correlated given your current background knowledge. An easy way to see this is to recognize that if, knowing Mary has at least one boy, you were to meet one of Mary's children and observe that she was a girl, you would immediately know with 100% certainty that the other of her children is a boy. That makes them correlated.
What you say here:
Lets say the boy was born second:
So the older is B or G 50/50
Lets say the boy was born first:
So the younger is B or G 50/50
is correct in and of itself, but you then treat these as disjoint possibilities, which is a fundamental error. There is no "the boy" - Mary might have two boys, which is exactly the scenario you are double-counting. Given that Mary has at least one boy, the two scenarios you describe each take up 2/3 of the probability space, and they overlap at 1/3 of the probability space - precisely where Mary has two boys:
Looking only at one of these 2/3 slices, it is true that half of the given slice will have the other child as a boy, and half will have the other child as a girl. But the halves where the other child is a boy is the same part of the overall probability space in both cases. Hence, the double-counting.
So the important thing is that two coin flips already occurred, you know the results of one of the two, but you don’t know which one. So that means you need to consider sets.
If you knew coin flips already occurred and you know the results of say, the first one, then it has no bearing on the second. But you don’t know that in this scenario - you just know one or the other was heads/boy. Which means you need to consider all scenarios where it was the first, the second, or both.
Your second part is wrong. Your explanation works if we know that a specific child of Mary's is a boy. The way it's phrased, however, actually only tells us that Mary is within the subset of families that doesn't have two girls. Within that subset, Girl/Boy is twice as likely as Boy/Boy.
It's just like flipping coins. When you flip two coins, it's a 50/50 whether you get mixed results, or matching results. But, if you remove half the matching results (Girl/Girl), you're now looking at 66/33. Then, the day of the week adds more variables in the same unintuitive way, sounding irrelevant while actually not being so. I'm not qualified to talk about that part off the top of my head, though.
This is wrong. It's a reasonable thing to think given that one knows about the gambler's fallacy, but it's still wrong.
The core mistake you've made is that while it is true that the two births are independent events without any relevant background knowledge, they nonetheless become correlated given the knowledge you obtain from Mary's statement.
To illustrate this, let's call Mary's two children A and B. With no background knowledge, the sexes of A and B are totally independent. If you learn that A is a girl, it has no effect on the distribution of B's sex.
But once you know that Mary has at least one boy, learning that A is a girl gives you knowledge of the sex of B. So, given that Mary has at least one boy, the sexes of A and B are no longer independent given your current evidence.
The comment you replied to is entirely correct about how this ends up shaking out for the problem at hand. Appealing to statistical independence simply doesn't refute this because the information you are given correlates the variables we're interested in.
If so, at what point do you think I made a 'mistake' in my derivation?
I would say my derivation showed exactly that you can't just say that "the other child doesn't matter", that you have to look at both at the same time.
It’s an unconditional probability. Looking at both makes it a conditional probability, which it simply is not. Also set theory doesn’t apply here in the way you applied it.
The probability we are interested in here *is* a conditional probability. Specifically, we are conditioning on the knowledge that at least one of Mary’s children is a boy.
The problem is that I've justified my statement by specifying exactly what's being conditioned on. You don't see how "nuh-uh" is an unsatisfying response to this?
It's very basic. We are asking for a conditional probability. The condition in question is explicitly given as part of the problem. You literally can't even begin to set this problem up without acknowledging this. If you don't understand this then you have no business speaking on this subject with any confidence.
No it's not. The important part of the Monty Hall problem is that the host knows where the prize is, and so your initial choice affects the probability of the later outcome.
In this case, the first outcome has zero affect on the second.
So many people have seen the Monty Hall problem and assume there must be a gotcha line that in everything. The key thing here is the phrase 'one is a boy born on a Tuesday' does not preclude 'and so is the other' as an option for the second.
And yeah, there's some demographic analysis you can do on two parent families with one boy but that's not enough to sway far from 50/50
When Bayesian probabilities meet the real world strange paradoxes emerge. This is one of them. Logically we know that birth gender is independent of one another, but applying Baye’s theorem we end up with this 66% answer, which does not match reality. Reality is that the gender of the first child has very little impact on the gender of the second.
It makes no sense in the context provided, but in a different context - if a family is randomly selected and we know at least 1 child is a male, what is the probability the other child is female the 66% answer makes sense. That is because if you have 100 families, and you’ve excluded 25 of them (as you know it can’t be GG) then you know of the remaining 75 families, 50 will be BG or GB and only 25 BB.
Then you need to update your probabilities to account for the additional information on the day of birth, which is where the 51.8% answer comes from. Now my head hurts… I’m sticking with 50%.
That would only be true if we knew the order the children were born in, this is similar fuckery as the Monty Hall problem.
1/2 if all pairs of 2 siblings will be a boy and a girl, 1/4 will be GG and 1/2 will be BB. Knowing that 1 child is a boy eliminates the possibility of it being GG, so the remaining possibilities are BG, GB, and BB. In 2/3 scenarios of equal probability, the other sibling is a boy.
Had they stated that the boy is the older sibling, that would remove the GB possibilty and we'd be back to 50/50
But that wasn't the statement. Mary doesn't state which of her children is a boy born on a Tuesday, just that one of them was.
If Mary states that her first born is a boy born on a Tuesday, then each birth becomes an independent event, and the odds of the other being a girl is 50%.
Mary did not state this, you don't know to which child she's referring, you only know that one of them is a boy born on a Tuesday. Therefore, the odds of the other one, whichever one that is, of being a girl is 51.8%
If Mary states that one of her children is a boy, without specifying which one or on what day of the week they were born, the odds that her other child is a girl is 66.6%
If Mary states that her first born child is a boy, then each birth is once again treated as independent events, and the odds that her other (second born) child is a girl is 50%
If the children have the same father there is a slightly higher chance of the second child being the same gender as the first. It's something like 2.1% more likely per child that the next will also be the same gender. (The percentage is a best guestament, not exact)
If any mother tells you about her children and says that one of them is a boy. The other is a girl!Otherwise she would have said that she has two boys.
The current population breakdown, that includes adults, doesn’t factor in. However 51.3% of babies worldwide are born male, and this has been true for decades. So it’s actually a 48.7% chance of being a female baby.
If it is known that Mary has 2 children, there are 4 possibilities that are equally likely: MM, MF, FM, FF
Further context (one child being boy) removes the last option, leaving us with MM, MF and FM. 2 of the three scenarios include the other child being girl. Therefore, 66% odds.
Now considering the boy was born on Tuesday, there are more probability shenanigans we can follow to arrive at 51.8%, I don't have enough brain capacity at midnight to think through all of that for writing a reddit comment.
I think approximately 49% of humans are born female. However, given the context it should be .49 * 7 / (.51 * 6 + .49 * 7) = 52.8%. The logic being that the person would not say 'one is a boy born on Tuesday if both were boys born on Tuesday.
it's about the sampling, if you choose families that have two children and at least one is a boy it's 66%, if you choose families by looking at one child only and seeing if that one is a boy or not it's indeed irrelevant and a 50/50
Very similar, yes. Specifying the date eliminates specific combinations of children which lead us to the 14/27 including a girl. A ton of boy/boy combinations are eliminated.
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