> You can't explain the difference without selective murder, lack of childcare, abortion or some other selective filtering.
I'd like to add that natural birth favors boys, citation: https://en.wikipedia.org/wiki/Human_sex_ratio#Natural_factor...
Not everyone will continue until they get a boy. Another child is an option, not a requirement. This is where the skew (can) come from.
The question is how likely are parents with G/GG/GGG to stop or try again.
No it can not! It's just mathematically and biologically not true, and attempts to erase a crime against humanity. The human inception process does not give a shit about your decision whether or not to put another child on this earth to decide whether the infant will be a boy or a girl.
Each child put on this earth has a ~50% chance of being either sex. It does not matter whether the parents decide to have another afterwards or not, this future child also has a ~50% chance of being either sex. The *only* variable that matters for the amount of girls that get born (in the absence of selective filtering) is the total number of children born, not whatever strategy their parents were going for.
To try and prove it to you, consider this randomized Python function:
import numpy as np
from numba import njit
@njit
def bear_children(stop_on_girl_p, stop_on_boy_p, max_children):
num_girls = num_boys = 0
while num_girls + num_boys < max_children:
child_is_girl = np.random.random() < 0.5
num_girls += child_is_girl
num_boys += not child_is_girl
r = np.random.random()
if ( child_is_girl and r < stop_on_girl_p or
not child_is_girl and r < stop_on_boy_p):
break
return [num_girls, num_boys]
def sample(n, stop_on_girl_p, stop_on_boy_p, max_children):
children = [bear_children(stop_on_girl_p, stop_on_boy_p, max_children) for _ in range(n)]
girls, boys = np.sum(children, axis=0)
return girls / boys
for max_children in np.arange(2, 5):
for stop_on_girl_p in np.linspace(0, 1, 5):
for stop_on_boy_p in np.linspace(0, 1, 5):
ratio = sample(10**6, stop_on_girl_p, stop_on_boy_p, max_children)
print(f"m {max_children}, g {stop_on_girl_p:.2f}, b {stop_on_boy_p:.2f}: {ratio: .6f}")
m 2, g 0.00, b 0.00: 0.999922
m 2, g 0.00, b 0.25: 0.995816
m 2, g 0.00, b 0.50: 1.001230
m 2, g 0.00, b 0.75: 1.001087
m 2, g 0.00, b 1.00: 0.999463
m 2, g 0.25, b 0.00: 0.997941
m 2, g 0.25, b 0.25: 0.999697
m 2, g 0.25, b 0.50: 0.999899
m 2, g 0.25, b 0.75: 0.997890
m 2, g 0.25, b 1.00: 1.001904
m 2, g 0.50, b 0.00: 0.999417
m 2, g 0.50, b 0.25: 1.002257
m 2, g 0.50, b 0.50: 0.997706
m 2, g 0.50, b 0.75: 1.003743
m 2, g 0.50, b 1.00: 1.002836
m 2, g 0.75, b 0.00: 1.001780
m 2, g 0.75, b 0.25: 1.001771
m 2, g 0.75, b 0.50: 0.997113
m 2, g 0.75, b 0.75: 1.001912
m 2, g 0.75, b 1.00: 0.998633
m 2, g 1.00, b 0.00: 1.000313
m 2, g 1.00, b 0.25: 0.997060
m 2, g 1.00, b 0.50: 1.001314
m 2, g 1.00, b 0.75: 0.997819
m 2, g 1.00, b 1.00: 1.003839
m 3, g 0.00, b 0.00: 0.999760
m 3, g 0.00, b 0.25: 1.000058
m 3, g 0.00, b 0.50: 0.999769
m 3, g 0.00, b 0.75: 1.003119
m 3, g 0.00, b 1.00: 0.999096
m 3, g 0.25, b 0.00: 1.000912
m 3, g 0.25, b 0.25: 0.999597
m 3, g 0.25, b 0.50: 1.000687
m 3, g 0.25, b 0.75: 1.001384
m 3, g 0.25, b 1.00: 1.001542
m 3, g 0.50, b 0.00: 0.999007
m 3, g 0.50, b 0.25: 0.999736
m 3, g 0.50, b 0.50: 1.001971
m 3, g 0.50, b 0.75: 0.999555
m 3, g 0.50, b 1.00: 1.000360
m 3, g 0.75, b 0.00: 0.999272
m 3, g 0.75, b 0.25: 1.001740
m 3, g 0.75, b 0.50: 1.001187
m 3, g 0.75, b 0.75: 0.998134
m 3, g 0.75, b 1.00: 1.002759
m 3, g 1.00, b 0.00: 1.002063
m 3, g 1.00, b 0.25: 1.002451
m 3, g 1.00, b 0.50: 0.999767
m 3, g 1.00, b 0.75: 0.999704
m 3, g 1.00, b 1.00: 1.003851
m 4, g 0.00, b 0.00: 0.999863
m 4, g 0.00, b 0.25: 0.998141
m 4, g 0.00, b 0.50: 1.000851
m 4, g 0.00, b 0.75: 0.999944
m 4, g 0.00, b 1.00: 0.999089
m 4, g 0.25, b 0.00: 1.001894
m 4, g 0.25, b 0.25: 0.998684
m 4, g 0.25, b 0.50: 0.999523
m 4, g 0.25, b 0.75: 1.000608
m 4, g 0.25, b 1.00: 1.003503
m 4, g 0.50, b 0.00: 1.000178
m 4, g 0.50, b 0.25: 0.998415
m 4, g 0.50, b 0.50: 1.000846
m 4, g 0.50, b 0.75: 0.999193
m 4, g 0.50, b 1.00: 0.998043
m 4, g 0.75, b 0.00: 0.999524
m 4, g 0.75, b 0.25: 0.999053
m 4, g 0.75, b 0.50: 0.996726
m 4, g 0.75, b 0.75: 1.000306
m 4, g 0.75, b 1.00: 1.000998
m 4, g 1.00, b 0.00: 0.999759
m 4, g 1.00, b 0.25: 1.000097
m 4, g 1.00, b 0.50: 1.000577
m 4, g 1.00, b 0.75: 0.999687
m 4, g 1.00, b 1.00: 0.996829When a couple has G, what's the probability they'll want to go for GX? When the couple has GG, what's the probability they'll want to go for GGX?
It doesn't matter that X is 50% boy 50% girl - in fact, it being 50/50 is why the bias ends up towards more G.
Edit: Ah wait I think I have something backwards in my head, I need to come back to this later. But I do want to mention that the estimated at-birth ratio in humans is more like 51:49, not 50:50
boys = 100000 girls 99350
boys = 100000 girls 100333
boys = 100000 girls 101195
In this process you will always get 1 boy, obviously. But you have a (1/2)^k * (1/2) chance of getting k girls before your first boy. Thus the expected number of girls is
Sum[k * (1/2)^k * (1/2), k, 0, inf]
Here are the results when the number of max births per family is dropped to 2:
boys = 74861 girls 75166
boys = 74752 girls 75464
boys = 75047 girls 74933
It doesn't matter what stopping criterion for your family composition you use, every child that gets put on the earth has a 50% chance of being a girl. Suppose you have children until you either get 5 or until you have a boy. The possible outcomes and their probabilities are:
If we sum up the average number of boys from this process, we get 1/2 + 1/4 + 1/8 + 1/16 + 1/32 = 31/32. If we sum of the average number of girls, we get 1/4 + 2/8 + 3/16 + 4/32 + 5/32 = 31/32. The expectation of boys and girls is exactly the same, as it must be!You can't explain the difference without selective murder, lack of childcare, abortion or some other selective filtering.