The fifth exam question passed Udacity's grader but I have strong reservations that it's actually returning the correct probability. Unfortunately, there is no definitive solution provided by Udacity to compare against, and the test cases that Udacity provides are not robust enough. I'll try to come back to it and give it another go at some point.  I also worked on question 4 which so far only needs an adequate successor fuction.
question 4 is spaghetti code right now, but im making progress
my program for question 4 now correctly answers the question but isn't fast enough to pass udacity grader. will check algorithm for improvements
Got question 4 to a point where it passes the Udacity grader by changing the successors function to only consider max moves by cars