binary trees binary tree is an ordered tree with the following properties every node has at most two children each child node is labeled as being either left child or right child left child precedes right child in the order of children of node the subtree rooted at left or right child of an internal node is called left subtree or right subtreerespectivelyof binary tree is proper if each node has either zero or two children some people also refer to such trees as being full binary trees thusin proper binary treeevery internal node has exactly two children binary tree that is not proper is improper example an important class of binary trees arises in contexts where we wish to represent number of different outcomes that can result from answering series of yes-or-no questions each internal node is associated with question starting at the rootwe go to the left or right child of the current nodedepending on whether the answer to the question is "yesor "no with each decisionwe follow an edge from parent to childeventually tracing path in the tree from the root to leaf such binary trees are known as decision treesbecause leaf position in such tree represents decision of what to do if the questions associated with ' ancestors are answered in way that leads to decision tree is proper binary tree figure illustrates decision tree that provides recommendations to prospective investor are you nervousyes no will you need to access most of the money within the next yearssavings account yes no are you willing to accept risks in exchange for higher expected returnsmoney market fund yes stock portfolio no diversified portfolio with stocksbondsand short-term instruments figure decision tree providing investment advice