facebook paradox

[kclick91]

Say there are two people with facebook accounts. Person A has 200 friends. Person B has 50 friends. It seems as though there is a higher probability that Person A has Person B as a friend than Person B has Person A as a friend. Of course, if person A is friends with person B then person B is friends with person A and vice versa. That would mean they would have the same probability of one having the other as a friend.

[John]

This isn't really a paradox. The difficulty arises from treating "A is friends with B" and "B is friends with A" as two separate events, whereas due to the way Facebook works, the two are really the single event "A and B are friends."

Edited September 17, 2014 by John

[CaptainPanic]

It is not a paradox.

 

Both number of friends (50 and 200) must be taken into the equation when you calculate the chance that A is B's friend and B is A's friend. The chance of both happening is actually the same.

 

The chance that A is friends with B is not calculated by just dividing 200 friends by the total number of Facetube members. If this were true, then A would have equal chances to be friends with a random person C living on a deserted island with only 1 facebook friend, and a particular person D having thousands of friends. But this is not true. He has a much larger chance of being friends with D than with C. This means that the number of friends of both people involved are needed to calculate the chance.