Answer¶
This means, on average, each of Marcia's friends have 49.5 friends. Including Marcia yields 50.5.
I also ran a simulation of 1,000,000 trials and achieved a similar result.
As of today, The Riddler Social Network is being rebranded as μετα — that’s mu epsilon tau alpha. Those Greek letters really augment the brand, don’t you think?
A group of 101 people join μετα, and each person has a random, 50 percent chance of being friends with each of the other 100 people. Friendship is a symmetric relationship on μετα, so if you’re friends with me, then I am also friends with you.
I pick a random person among the 101 — let’s suppose her name is Marcia. On average, how many friends would you expect each of Marcia’s friends to have?
Every person has a 50 percent chance of being friends with each of the other 100 people. This means, on average, everyone has 50 friends.
Given Marcia's friend circle, everyone has at least one friend, that is, Marcia. And they have a 50 percent chance of being friends with each of the other 99 people.
This means, on average, each of Marcia's friends have 49.5 friends. Including Marcia yields 50.5.
I also ran a simulation of 1,000,000 trials and achieved a similar result.