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No it's not. As far as we know the chance of a child being male or female is 50% (not quite, but I'll assume it for simplicity here), independent from any previ

No it's not. As far as we know the chance of a child being male or female is 50% (not quite, but I'll assume it for simplicity here), independent from any previously born children. That is, it is a 'memoryless' process, and you've fallen for the gambler's fallacy. Just because you threw many tails before does not increase the odds of heads. 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: B (1/2), GB (1/4), GGB (1/8), GGGB (1/16), GGGGB (1/32), GGGGG (1/32) 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.

a_conservative 5y ago
If anyone is unsure of the truth of the parent post (like I was), I built a simple simulator in Python to test it for myself [0] boys = 100000 girls 99350 boys = 100000 girls 100333 boys = 100000 girls 101195 [0] https://pastebin.com/Et5CU3n0 https://pastebin.com/Et5CU3n0
- nightcracker 5y ago
  You simulated the limiting case, where you don't stop having babies until you get a boy. That's (obviously) not realistic as we have a finite lifespan and fertility, but note that the expectation still holds. 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] which is 1: https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%5Ek+*+%281%2F2%29%2C+k%2C+0%2C+inf%5D https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%... .
  - a_conservative 5y ago
    Excellent point! I updated it to make the number of births per family a parameter. It's still an approximation of reality of course. 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
Izkata 5y ago
You are noticeably missing G, GG, GGG, GGGG... 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.
- nightcracker 5y ago
  > This is where the skew (can) come from. 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] Now let's plot the ratio of girls to boys for one million samples to this function for various stop probabilities on girls, boys for a maximum of two, three or four children: 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}") What are the results? As predicted, a complete indifference to parental strategy: 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: 0.996829
Koiwai 5y ago
Ha, I've argued this math in multiple situations. > 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_factors https://en.wikipedia.org/wiki/Human_sex_ratio#Natural_factor...

a_conservative 5y ago

If anyone is unsure of the truth of the parent post (like I was), I built a simple simulator in Python to test it for myself [0] boys = 100000 girls 99350 boys = 100000 girls 100333 boys = 100000 girls 101195 [0] https://pastebin.com/Et5CU3n0 https://pastebin.com/Et5CU3n0

nightcracker 5y ago
You simulated the limiting case, where you don't stop having babies until you get a boy. That's (obviously) not realistic as we have a finite lifespan and fertility, but note that the expectation still holds. 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] which is 1: https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%5Ek+*+%281%2F2%29%2C+k%2C+0%2C+inf%5D https://www.wolframalpha.com/input/?i=Sum%5Bk+*+%281%2F2%29%... .
- a_conservative 5y ago
  Excellent point! I updated it to make the number of births per family a parameter. It's still an approximation of reality of course. 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

Izkata 5y ago

You are noticeably missing G, GG, GGG, GGGG... 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.

nightcracker 5y ago
> This is where the skew (can) come from. 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] Now let's plot the ratio of girls to boys for one million samples to this function for various stop probabilities on girls, boys for a maximum of two, three or four children: 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}") What are the results? As predicted, a complete indifference to parental strategy: 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: 0.996829

Koiwai 5y ago

Ha, I've argued this math in multiple situations. > 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_factors https://en.wikipedia.org/wiki/Human_sex_ratio#Natural_factor...