A list of $n$ items is arranged in random order; to find a requested item, they are searched sequentially until the desired item is found. What is the expected number of items that must be searched through, assuming that each item is equally likely to be the one requested?
Attempt: The number of searches $X$ follows a geometric distribution with $p = \frac{1}{n}$ (each item is equally likely to be selected). The expected value of a geometric distribution is $\frac{1}{p}$, thus
$$ E(X) = n$$
I couldn't verify this answer in my textbook or online so hopefully someone here can help out.
There is no Geometric Distribution here...the trials are not independent.
As the object has an equal chance to be in any position, $$E=\frac 1n\sum_{i=1}^ni=\frac {n(n+1)}{2n}=\frac {n+1}2$$