Thread: statistics plz help with the kings paradox

im a king

yes the king of my house

as so is my father and his father and his father and so on for 8000 generations, the time we left caves

i suppose you have not trouble in believing theres an interrupted lines of kings of the house in my family

after all is just natural to have a father and a grandfather and a grandgrand father and so on till very far

in fact the fact i descend from an uniterrupted line of males is 100%

but lets play with statistics lets look it the other way around:

what are the chances that my always paternal ancestor from 8000 generations away had an uninterrupted linage in which every generation happen to have a son

lets suppose there are 50% chances to have a boy for every generation

so that every generation has a boy the statistics say it will be 0.5 elevated at 8000

if you introudece that number in a calculator it says chances are 0

so in one hand the chances i can trace myself an uninterrapted male lineage is 100%

but the chances my paternal antecesor form 8000 generations away had a line in which every generation had males is 0

plz can somebody help me with my confusion?

oh maybe im not confused and the statistics im here is zero, and that together with being the winning spermatozoid of millions makes me quite unique, and always descendant of winning spermatozoids

and the statistic we are all here is 0/6 billion

The first problem is assuming that the chance would be 50/50. If it's just "has a male child" instead of "first child is male," the chance is complicated, but better than 50/50. The second problem is in trusting your calculator so completely. is a very small number, but not 0.

Edit: Cut some stuff out I wasn't quite sure of, being too sleepy.

my point is to prove statistics fail for being deterministic in analizing an undeterministic fact as reproduction, if you allow me ill think aloud:

what are the chances that being everything fine humanity survives 8000 generations, 120000 years?

lets suppose humanity survives for 8000 generations, all males from the future can trace a line dad grandad grand grandad and so on with males for 12000 years

this means with no doubt that theres at least one person now with at least one line that goes 8000 genearations into the future all males, from grand grand father to grand father to father to son

so for the survival of humanity during 8000 geneartions is indispensable that now theres at least one person with at least one line that continues to the future with every generation having at least one boy

so lets calculate the chances this requisite is acomplished in the present so humanity can last 120000 years at least:

that one man from nowadays have children theres a 50%, and that that man has at least one boy will be the 50%of 50%, a 25% of posibilities for a man to have a boy

now what are the posibilities that a line for 8000 generations all generations have at least one boy always

it would be a posibility of 0.25 elevated to 8000, that multiplied by 3000 millions of men there are now

gives a posibility of 3000 millions*(0.25 elevated to 8000)

so for the requisite that humanity exists in 12000 years is proved that it must be acomplished, that there is now at least one person who will have a 8000 generations of all males genealogy, if this is not acomplished there just wont be humanity

and the chances of this are almost 0 with which statistics contradicts facts

with which the deterministic aproach of statistics fails on analizing nature since nature is indeterministic

It's like shuffling a deck of cards and then asking what are the odds of getting that particular order of cards. The answer is "close to zero," and yet there it is.

yes the chances of getting that determined order is close to 0 but the chances of getting any order is 100%

i think i proved using statistics that the posibility of future existance of humanity with reproduction is close to 0

i didnt calculate the posibilities of getting a certain person instead of other, more similar to your analogy

but the posibilities of getting any person more similar of my analogy of getting any combination

i used statistics to calculate chances of existance of people in 8000 generations

if statistics says the posibilities are close to zero statistics are wrong

what are the odds that, out of children, EVERY one will be female? You're fallacy comes from assuming that an unbroken line of males is seemingly impossible, when, given an average of, say, 2 children, there's a 75% chance that there will be a son; an average of 3 children gives an 87.5% and so on and so forth.

allow it to be 2 children, we have so the odds are massively better, comparatively speaking. Allow it to be 3 children and we have which is, again, massively better. Let's say that for 4000 generations the average is much high than the other 4000 generations, where there is an 8 child per couple average. We have great odds that atleast one child is a male now: alright. That's kinda low, but not nearly as low as you're original figure, and you multiply that with what ever the average would be of the second half.

Originally Posted by luxtpm

yes the chances of getting that determined order is close to 0 but the chances of getting any order is 100%

Yes, just like the odds of getting SOME male line out of all the people in the world is close to 100%, even though the odds of getting any SPECIFIC line is very low.

according statistics the chances i have some male line uninterrupted during the next 8000 generations:

supposing me and every male has a 99%posibility of having at least one son

the chances every generation during 8000 generations all happen to have at least one male ( a must for the survival of the specy during 120000 years) is:

0.99elevated to 8000

and the chances of all the males from today to have some male line that lasts 8000 generations is

3000 millions*(0.99elevated to 8000)=

3.6*10 elevated to -21

those are the chances per 1 of survival of this humanity via reproduction using statistics and being very generous, though i know that with no disaster posibilities are almost 100% of survival

i wished i had a 99% chance of having children

i see the issue better an better thanks:

human reproduction implies there will be a male chain(as well female) ...grandfather father son,if the chain breaks we can not exist

the chances of a chain like this all males to exist is equal to the chances to have borned a boy elevated to the number of generations that extend in the future

No, the chances of you having an unbroken male line for the next 8000 generations is not the same as the chances of there being some unbroken male line for the previous 8000 generations. (You wouldn't be here if there wasn't some line.)

Even so, no specific line has to remain unbroken for the next 8000 generations for there to be males in each generation. Again, an unbroken line of ancestors isn't the same as an unbroken line of descendants, at least not from a probability point of view.

Originally Posted by luxtpm

according statistics the chances i have some male line uninterrupted during the next 8000 generations:

supposing me and every male has a 99%posibility of having at least one son

the chances every generation during 8000 generations all happen to have at least one male ( a must for the survival of the specy during 120000 years) is:

0.99elevated to 8000

and the chances of all the males from today to have some male line that lasts 8000 generations is

3000 millions*(0.99elevated to 8000)=

3.6*10 elevated to -21

You are calculating it as though each male in a generation could only produce either a single male child or zero male children, in which case the male population would indeed slowly shrink. Fortunately people can have more than one child.

More realistic numbers would be along the lines of each of the 3*10^9 males today producing an average of 1.1 male children, so we have 3.3*10^9 males in the next generation.

im not talking the probability we survided the last 120000 years, this is 100% probability

im talking of the probabilty we survive another 120000 years via reproduction being everything fine

if we are going to survive that will mean there will go 8000 generations

all those people from the future will be able to tell they all had at least one relative from our present exclusivily related by paternity ... the grandfather of the father of the son

so that theres humanity in the future implies that now theres at least one person whos gonna have a linage of 8000 generation in which in every generation it doesnt fail to have at least one boy,the grandfather of the father of the son


to realize of the improbability of a long line all male think of kings who have only daughters

or family names inherited only from father to son how soon they get lost

and as explained that humanity survives implies theres now at least one person whos gonna have an unbroken line of males, father son, not father daughter who marries another man

this probaility is extreamly low yet we know intutivily that the posibilities humanity srvives there being everything fine is almost 100%

"You are calculating it as though each male in a generation could only produce either a single male child or zero male children, in which case the male population would indeed slowly shrink. Fortunately people can have more than one child. "

well its true im ignoring that

but what im searching is the posibility that from now i develope a timeline all male, which is a must for reproduction since we evolved from one and only one timeline all males besides many others

and once found my posibilities of developing a time line all males that lasts multiply it by all males of humanity

i think we should agree that the posibilities of my family name only inherited from father to last 120,000 years is quite remote not to mention 2 million years

The odds of one specific family line being all male is somewhere between 0 and 100. The odds of humanity ending for lack of males is nearly 0.

Let's do a few examples. Let's say each couple has 2 children, and generations are somehow synchronized, for simplification sake.

In the first question, we start with a specific couple. There's a 25% chance that the line ends there, when they have two daughters. There's a 50% chance of there being exactly one son, and a 25% chance of there being two.

If there's one son, the next generation is an exact repeat of this scenario. If there's two though, the chances of the line continuing improves. Both sub-lines would have to end for the whole line to end.

Let P be the probability of the line continuing. Then P = 0.25 * 0 + 0.5 * P + 0.25 * (1 - (1 - P)^2). Rewriting gives -P^2/4 = 0, or P=0. In other words, under these simple assumptions, the chance of a particular individual's male line continuing forever is 0. That doesn't say anything about how long it'll last though.

On the other hand, the only way humanity would end would be if every child in one generation was female (or male). (Actually, all females could probably survive on artificial methods much better than an all male generation, but that's beside the point.) Let's say there are 4 generations alive at any one time and 6,000,000,000 people on the planet. Then each generation would be 1,500,000,000 people. The chance of the next generation being all female would be (1/2)^(1500000000). The chance of this happening in the next 10000 generations would be, 1 - (1 - (1/2)^(1500000000))^(10000). Again, this is a simplification, since the size of each generation would be dependent on the last, but you can start to see why this isn't likely.

Edit: To approximate that number, (1 + 1/x)^(nx) is about e^n. Using this, (1 - (1/2)^(1500000000))^(10000), n would be -10000/1500000000 or -1/150000, so that probability would be about 1 - e^(-1/150000), if I did my math right at least.

Edit again: Oh yeah. I should also point out that the fewer males, the more likely their lines are to continue, assuming humanity continues. If there was only one male, the entire next generation would be of his line, as would any future generations, so his line would be guaranteed to continue as long as humanity did.

" The odds of humanity ending for lack of males is nearly 0. "

this is not what im saying

what are the chances my last name inherited only from the father lasts 2 million years?

the same chance i have to have a line that goes from father to son unbroken, always males, not a father that has a daughter who marries another man,but father to son during 2 million years

quite a remote chance

then how comes everybody in the future has one and only one exclusivily paternal line, the oddity

hadnt we say that the chances of a line exclusivily paternal for 2 million years is almost 0?

"More realistic numbers would be along the lines of each of the 3*10^9 males today producing an average of 1.1 male children, so we have 3.3*10^9 males in the next generation."

this is the most challenging answer:

that 0.1 of extra male children are gonna die and their line extint if the popultation is to remain constant, most probable due to limited resources

if they die before the 8000th generation they have a 0% of acomplish exclusive paternality through 8000 generations so they just dont count

luxt, that doesn't even make sense

Uh, males have to have sex with females in order to reproduce. Also, each new generation is so much larger because they have new families changing the probability of having a male.

So unless your entire line of ancestry only reproduced via incest, what you are saying doesn't seem to have any meaning.

EDIT: What I am trying to say is, on family can easily make more than one person which then goes on to make another family, which can also produce more than one person. Each time there is a new generation, it is usually larger. This exponential growth is much faster than the exponential shrinking of the probability of having a male.

:-D

i find extreamly odd you have a father of your father of your father of your father... that goes back 2 million years

you must find this stupid but i find it odd

a line of father son father son never unbroken with father daughter seems very rare to me

what are the chances i create a line that extends 2 million years in the future of unbroken father son?

hell i even have remote chances of just making a line that lasts that long, then what are the chances this line is all father son?

i think ive found the answer to my question:

my father has an original last name that he took from my name as he signed his maths books with this name

what are the chances this last name lasts undefinly? or what is the same what are the chances my father breeds unbroken lines of males from father to son and not from father to daughter?

first if humanity population is to remain constant everybody will have a media of two children plus a 0.1 who will die childless so i just wont count them

so my father tosses a coin two times heads a girl tails a boy

for every time he gets a tails he has two extra tosses, like for every male he has this male has two chances of having a boy, two more coin tosses

try this game to find your chances of having an ubroken lines of males so your last name lasts

you start with only two tosses and for every tails you get you have two extra tosses, when you have no more tosses you lose

try it and youll see the chances we all have of having an unbroken lines of males is something like 75%

then the thing about the mithocondrial eve is bs

since for this she should be the only female of her time to have an unbroken lines till our days of females, mother to daughter while every female of her time had a chance of doing this as well of 75%

The mitocondrial eve is pretty well established. Sometime long, long ago (I forget how long) there existed a woman that all living humans could trace their ancestry back to. This doesn't mean she was the only woman alive at the time, just that her family line (mitocondria are passed down from the mother) came to dominate the others.

For your game, I've already worked out chances of the game lasting forever. It worked out to 0. Check my math though, I might have done it wrong. Like I said though, that doesn't say anything about how long it will last.

still wonder if probability can be aplied to human reproduction:

on the one hand to know the probaility of every female to have a matriarcal line till our days she could play that tossing the coin game, it seems to me a quite high probability

on the other hand as you go up on the line every time two sisters have a same mother it will reduce the number of females candidates to have a matriarchal line

so either theres a contradiction here or my tossing the coin game is not the accurate representation of my posibilities of stablishing a patribility line and that my last name lasts

any suggestion on how to find my posibilities that my last name lasts?

Yes, probability can be applied to these questions, but the answers are much more complicated than what you're thinking they'll be.

As for the question, will your last name last, your coin tossing game is basically the right idea, but you need to do your math more carefully. Actually, for the question, will it last forever, I already did the math (your game and my scenario are equivalent) and came up with a 0 probability. I haven't answered the related (but much harder to work) problem of will it last n generations, or how many generations would you expect it to last.

Edit: I should point out that something that goes to 0 at infinity might still be positive everywhere (consider 1/x). So even if there's a 0 probability of your line lasting forever, there might still be a chance of it lasting any finite amount of time.