You are given a minimum heap, with probability going to left is 50% and going to right is 50%. What is the probability that You will land up on a maximum element in the heap? For this scenario since going to right and left have equal probabilities we can state the answer to be $(1/2)^{O(\log n)}$ .As at each step we have two possible decisions and we can choose the correct path with a probability of 1/2. We have to make this decision $\log n$ number of times (height of the heap).It doesn't matter whether we take a left or a right from the present node as both are equally probable.But if the probabilities are not equal for left and right is this model still valid?The Question How can we model the above situation where the probability of going to right is $x$ and to the left is $1-x$, where  $0<x<1 $ Is the concept of random walks on graphs involved?Assumptions :There exists a unique maximum element which by the definition of heaps exists at some leaf node.
Probability of finding the maximum element in a heap
data structures;probability theory;heaps;random walks