Expected values with choosing involved Hi I was working on this question for my exam review:

A jar contains $17$ red balls and $5$ blue balls. Repeat the following
  $12$ times: Choose one ball uniformly at random (and leave it in the
  jar). Let $X$ be the random variable whose value is the number of blue
  balls that we choose. What is the expected value $E(X)$ of $X$?

The textbook answers page says $\frac{30}{11}$ but I have no idea how it ended up with that answer even though understand the basic concept of expected value any help?

Since $X\sim \mathrm{Bin}(n=12,p=\dfrac{5}{22})$, then you need to find
$$\sum\limits_{x=1}^{12}x{12\choose x}\left(\dfrac{5}{22}\right)^x\left(\dfrac{17}{22}\right)^{12-x}$$
Luckily, since it is well known that $E(X)=np$, for $X\sim\mathrm{Binomial}$ then that's all you need to calculate
