There are $n$ people. The probability that each pair of people is friends is $p$, independently. What is the expected number of pairs who are friends?
Am I crazy for thinking this is just $n \choose 2$$\cdot p$?
There are $n \choose 2$ distinct pairs of people, and the probability that any pair is friends is $p$ independently, so can we just use linearity of expectation to arrive at this result in this way? What am I missing?
No, you are not crazy. This is an application of the linearity of expectation. Of course, the claim that the probability two people are friends is independent of them having mutual friends is not the way the world works, but that is what you are given.