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?



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?

No. This does not follow. Your confusion is this:
Among all people, there are indeed just as many of type $A$ as of type $B$. Indeed, it is in this sense that $A$ and $B$ are equally likely.
But among all friends, there are $4$ times as many $A$'s than $B$'s. So, picking from all friends, you can expect $4$ out of $5$ to be of type $A$
