time complexity – answers Average case analysis of linear search

Suppose we have an array$(1..n)$ and run linear search to find $x$, on it with following specification:
probability of existence $x$ in first half of array is $p$,and probability of existence $x$ in second half is $3p$ and in each half probability of any element to be x is equally likely.Calculate Average case linear search.
Is my answer true?

$E(successful)+unsuccessful=sum_{i=1}^{n/2}pi + sum_{i=frac{n}{2}+1}^{n}3pi + (1-p)(1-3p)n $