(From Sholander24) In a standard clover-leaf interchange, there are four ramps for making right-hand turns, and inside these four ramps, there are four more ramps for making left-hand turns. Your car approaches the interchange from the south. A mechanism has been installed so that at each point where there exists a choice of directions, the car turns to the right with fixed probability r.
(a) If r = 1/2, what is your chance of emerging from the interchange going west?
(b) Find the value of r that maximizes your chance of a westward departure from the interchange.