Average number of comparisons to locate item in BST
Recall, how expected value is defined. You count the for every element $X$ in the tree the number of comparisons it takes to locate it, say $C(X)$. Then
$$E[\text{# of comparisons}]=\sum_{X\in\{A,\ldots,H\}} p_X \cdot C(X),$$
where $p_x$ denotes the probability that $X$ is chosen, which is the same for all $X$, namely $1/8$. In other words, you compute the average over the $C(X)$s.