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# Having sisters

## Question

Do men have more sisters then women?

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No.

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Hard to say. Of course, each woman can count several times, if she has several brothers.

Judging from the sample of population just around me, the answer is NO. However, that may not be accurate, since I am surrounded by people with zero, or one sibling.

Most men I've met have no sisters. Of those who do, most have just one sister. And the general assumption here is that there are about the same number of men and women overall.

Edited by Prime
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Let's take a global average and say that in average, in a family there are N boys and M girls. Then, each of the N boys have M sisters and each of the M girls have M-1 sisters.

Therefore, in average men have more sisters than women.

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@DeGe I think you got caught in his cleverly designed trap

Lets try a family of three for an example. If there is the same chance of having boys as girls the following family constructions from oldest to youngest are equally likely.

Family Construction Girls v Boys
GGG 3 girls * 2 sisters v 0 boys * 3 sisters = 6v0
GGB 2 * 1 v 1 * 2 = 2v2
GBG 2 * 1 v 1 * 2 = 2v2
GBB 1 * 0 v 2 * 1 = 0v2
BGG 2 * 1 v 1 * 2 = 2v2
BGB 1 * 0 v 2 * 1 = 0v2
BBG 1 * 0 v 2 * 1 = 0v2
BBB 0 * 0 v 3 * 0 = 0v0

Total Girls = 12 Total Boys = 12

I'll leave it to you to figure out the formula to use for an arbitrary family size.
Edited by phaze
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@bmad: I do not think my answer was the best one - after all, the chances were 50-50

phaze answered much better, he explained WHY.

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Fair enough

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I think it is still up for grabs, as I have not proven anything but simply given an single example.

The prize should go to anyone who can come up with an explanation for families of arbitrary sizes rather than of size 3

Hint: Pascal triangle

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For any n, the probability of having n sisters is independent of your own gender. Hence your expected number of sisters is also independent of your own gender.

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I think it is still up for grabs, as I have not proven anything but simply given an single example.

Myself, I would prove it for N=0 and leave the proof for N>0 to the reader If you try for some N, you quickly see the law.

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Do men have more sisters then women?

As stated it depends on how many women the average man has.

In my case, I have two sisters, and the second part is classified.

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I suspect the OP really asks: "On average, who have more sisters: men or women?"

Then the answer seems to be: Men have more sisters than women (do).

A similar, seemingly true statement is: Men have more sisters than (they have) brothers.

Proof:

In every family, there are m male children and f female children.

Assuming mf =/=0, the m male children each have f sisters; the f female children have (f-1) sisters.

Similarly, every female child has m brothers.

Since f > f-1 and on average m = f, both statements are true.

But do the statements hold true for weighted averages across populations?

Let's distribute an equal number (25) of sons and daughters among three families, as follows:

Family 1: m=f=10. 10 men each have 10 sis and 9 bro; 10 women each have 9 sis.

Family 2: m=2f=10. 10 men each have 5 sis and 9 bro; 5 women each have 4 sis.

Family 3: 2m=f=10. 5 men each have 10 sis and 4 bro; 10 women each have 9 sis.

25 men have 200 combined sisters and 200 combined brothers;

25 women have 200 combined sisters.

On average, the men have 8 sisters and 8 brothers; the women have 8 sisters.

Both statements are false.

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According to chinese rules that held for a long time, you can have only one child. But if it is a girl, you can have a second one.

If the rules are respected, out of 4 families, 2 have one boy only, 1 has one boy and one girl, 1 has two girls.

The 3 boys have 1/3 sister on average, the 3 girls have 2/3 sisters on average.

Since China represents a non-negligible proportion of the world population, it would seem girls have more sisters on average.

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@Grimbal

You can continue:

- there are 50.5 boys born per 49.5 girls.
- women live longer.

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