Gender distribution probability
Suppose there are N male and N female students. They are randomly distributed into k groups.
Is it more probable for a male student to find himself in a group with more guys and for female student to find herself in a group with more girls?
The question is motivated by an argument with my mother. She claimed that in the majority of collectives where she was, the number of women besides her was greater than men, while I had the opposite impression, that in most collectives where I was a member there was more men even if not to count myself.
I never was in a majority-girls collective, so I think for a male it is more probable to find oneself in a majority-male collective (even if we exclude oneself).
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There are essentially three perspectives you can take:
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Without further information, any group is as likely to have more of either sex.
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Consider a group that has you, a male student, in it. It is now more likely for it to be dominated by men, since it has one man (you) and the remaining k-1 people are chose randomly from among N-1 men and N women.
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Considering a group where you are, and excluding you but looking at the other group members, they are chosen from among N female and N-1 male students, so it is (slightly) more likely for a majority of them to be female.
You can calculate the probabilities by using the hypergeometric distribution.
However, the motivating observation could be explained by paying more attention to the group composition when you are in the minority.
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