There is a set $V=\{1,2,...,n\}$-it may be considered as a vertices of a graph we build.
We pick at random independently a pairs of different elements from $V$. This makes a set of edges $\mathcal{E}$
For each pair $\{i,j\}$ probability that we pick it is equal to $p$
This makes a graph $G=(V,\mathcal{E})$
Now, let's consider a function $f$ that works in following way $f(G)=a$, where $a$ is a minimal amount of vertices that we have to remove in order to get a new graph without any $k$-cliques
Calculate $E[f(G)]$
Regards