In the worst case, a binary search tree is skewed. The depth of such a tree would be O(n).
The worst case would occur when the key values are added to the binary search tree in a sorted order.
But in the average case, the key sequence won't be sorted — it'd be a random mix, which gives us O(logn) depth in the average case. Option C.
Bonus:
Even in the worst case, the depth of balanced binary trees like AVL trees is O(logn).