I am working on a proof that require the result of the following problem:Let, $T$ be a rooted directed tree with height $h (\ge \lceil{log_d{n}}\rceil )$ and having $n$ nodes. Each internal node of $T$ has degree (# of children) at most $d$. $T$ was picked uniformly at random from all possible such trees. We define a decent on $T$ as follows.  Start with root, for each of its children we decide with probability $p$ whether to decent the subtree rooted by that child. This decisions are made independently for each of the children of root. Then the process continues recursively. Then, what it is the average number of nodes this procedure will visit?Is there any known result for this problem for trees with $d$ > 2?
On a property of random rooted trees with $n$ nodes and of height $h$
ds.data structures;tree