Answer
See below.
Work Step by Step
By definition, the expected value is the sum of each outcome multiplied by its probability. (The possible outcomes are $\{BB,BG,GB,GG\}$, where $G$ stands for girl and $B$ stands for boy.
Hence here the expected value: $\frac{1}{4}\cdot2+\frac{2}{4}\cdot1+\frac{1}{4}\cdot0=1$.
This means that if we take the average number of girls for a lot of families with two children we are expected to get a number close to $1$.
