Answer
$\frac{4n+6}{6}$
Work Step by Step
We have to find the average-case computational complexity of the linear search algorithm if the probability that $x$ is in the list is $p$ and it is equally likely that $x$ is any of the $n$ elements in the list.
$E=p(n+2)+ (2n+2)(1-p)$
Substituting $p=\frac{2}{3}$, we have $E=\frac{2(n+2)}{3}+\frac{(2n+2)}{3}=\frac{4n+6}{3}$
