Consider a graph a containing n nodes in which s < n nodes have been explored in the forward direction and backwards direction by bidirectional search (Figure 2.6). The graph contains a single starting state and a single goal state. What is the probability that forward search contain the single goal state? What is the probability that the forward and backwards search have at least one node in common, assuming that forward and backward search each reach a random subset of s nodes. Use this analysis to discuss why bidirectional search is likely to be more efficient.