I am trying to solve this question by using the reflection principles.
Let a>c>0 and b>0.
A is the set of all paths of a random walk which end at c in their final n’th step.
B is the set of paths from A which first hit a and then -b.
C is the set of paths from A which first hit a and then avoid completely -b.
D is the set of paths from A which avoid –b completely before hitting a for the first time.
Write out properly in mathematical notation the sets A, B, C and Find their respective probabilities in terms of a, b, c and n..