Problem source

The cakes in our canteen each contain
exactly four currants, each currant being randomly placed in the cake. I take a proportion $X$ of a cake where $X$ is a random variable with density function
\[{\mathrm f}(x)=Ax\]
for $0\leqslant x\leqslant 1$ where $A$ is a constant.
\begin{questionparts}
\item What is the expected number of currants in my portion?
\item If I find all four currants in my portion, what is the probability that I took more than half the cake?
\end{questionparts}