In this question, we have a person trying to cross the river. However a night before that, there is a storm and each bridge has 50% chance of being struck by lightning strike unconditionally from the previous lightning strike. This would destroy and bridge. What is the probability that there exists a path to cross river?
(As you can see in the drawings, we have 13 bridges, some of then cross at one of the 6 junctions)
Firstly I just tried adding all the possibilities together and computing the probability of two vertical bridge move (1/4) and probability of (two vertical and one horizontal - 3/8) in the end both of these computations were wrong because the issue here is that there is a lot of overlapping, i.e. if there is 2+ routes, this overlapping event made me confused and stuck and any progress I made, or any pattern I tried to spot came back to the questions how do I get all the possibilities without actually writing all of them down. Thanks for any help