i have been attempting to do this problem as part of an exam review but having some trouble
Let {Xn} be a simple random walk on the integers with a probability of .4 of moving to the right.
a) If X0 = 3, find the probability that the walk ever reaches 8.
b) If X0 = 1, find the probability that the walk ever reaches -10.
c) Now consider the same random walk, but with a reflecting boundary at 6. If X0 = 4, what is the expected number of steps until the walk reaches 3?
So far I have found this formula: (1 -(q/p)^x)/(1-(q/p)^a) and found that question a could be 0.0964 and question b was infinite as it came up to be a negative number