An investor has a stock that each week goes 50 cents up with probability 50% or 50 cents down with probability 50%. She bought the stock when it costed $25 and will sell it when it reaches $55 or falls to $5. (a) What is the probability that she will sell it at $5? (b) Find the mean number of weeks the investor keeps the stock. (c) Find the probability that the price of the stock will again be $25 before the investor sells it. (d) How many times, on average, will the price of the stock return to its initial value of $25 before the investor sells it? Show your work.