A full binary tree of height 4 has 15 nodes, as pictured below.

(attached later)

The 8 nodes at the bottom of the tree are called end nodes or leaf nodes. Two distinct end nodes are uniformly chosen. The expected length of the shortest path between them can be expressed as ab, where a and b are coprime positive integers. What is the value of a+b?

Question

A full binary tree of height 4 has 15 nodes, as pictured below.

(attached later)

The 8 nodes at the bottom of the tree are called end nodes or leaf nodes. Two distinct end nodes are uniformly chosen. The expected length of the shortest path between them can be expressed as ab, where a and b are coprime positive integers. What is the value of a+b?

anonymous · Answer

attachment

loser66 · Answer

in which order? pre-order? post-oder or in-order? need more information. 
to me, you should label nodes, and count the length of each node. depends on which order they ask you to consider ab and a+b