Suppose you are standing on the bank of a straight river.
(a) Choose, at random, a direction which will keep you on dry land, and walk 1 km in that direction. Let P denote your position. What is the expected distance from P to the river?
(b) Now suppose you proceed as in part (a), but when you get to P, you pick a random direction (from among all directions) and walk 1 km. What is the probability that you will reach the river before the second walk is completed?