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Friendship paradox (Posted on 2014-10-31) Difficulty: 3 of 5
Most people have fewer friends than
their friends have, on average.

Prove it.

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: n = 721,000,000: Intuitively Comment 4 of 4 |
(In reply to n = 721,000,000 by Steve Herman)

If there are two classes: one with 10 students and one with 30 students, you are 3 times more likely to be in the large one.

If there are 3 flights with 100, 200 and 300 people you have a 50% chance of being on the largest flight.  In fact 50% of the people will be.  So while the average flight size is (100+200+300)/3 = 200, the weighted average of people on your flight is (100²+200²+300²)/600 = 233.
And if you say "I never seem to be on a nearly empty flight."  Realize that it's a minority of who people do.

With friendships it's the same, but you have to look at non-friendships.  In a group of people, some might be friends with almost everyone else (low non-friendships).  But most people will not because every time a potential friendship is missing it is missing for two people.

  Posted by Jer on 2014-11-03 09:30:35

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