Picking a popular vs unpopular friend There are 2 types of people on a social media platform: type A has 80 friends, type B has 20 friends. 
We assume that half of the people are Type A, and half of the people are Type B. 
The expected number of friends for a person is then $\frac{1}{2} \times 80 + \frac{1}{2} \times 20 = 50$.  
What is the probability I pick type A friend among my friends? This question is taken from this Udacity video. 
Their answer is explained here. They state the probability of picking type A friend among your friends is $\frac{4}{5}$. 
I understand their reasoning, and it makes sense - it is much more likely to have a "popular" i.e. type A friend among your friends than "unpopular" i.e. type B friend, simply because their probability of having you as a friend is higher. 
But I am wondering why we can't reason like this: 


*

*type A and type B people are equally likely as stated above. So among my friends, I am as likely to pick type A person as type B person?


In the overall population if a person is selected at random, they are equally likely to be Type A or Type B. However, your friends circle is not representative of the overall population.
It's like say half of all people in the world are rich and half are poor. A guy walks up to you in the street and gives you one dollar for your service. Is he equally likely to be rich or poor? No, he is not a random representative of the population
