13 We are going to see the movie Fatal Repulsion. There are three parking lots we may park in. One is one block east of the theater (call this lot 1); one lot is directly behind the theater (lot 0); and one lot is one block west of the theater (lot 1). We are approaching the theater from the east.

There is an 80% chance that lot 1 will have a vacant space, a 60% chance that lot 0 will, and an 80% chance that lot 1 will. Once we pass a lot, we can’t go back to it. Assume that when we are at a given parking lot, we can determine whether it has any vacant spaces, but we can’t see any of the other lots. Our dates for the evening will assess us a penalty equal to the distance (in blocks) that we park from the theater. If we find no space, they will assess a penalty of 10 (and never go out with us again). What strategy minimizes our expected penalty? Answer the same question if there is a 70% chance that lot 0 has a vacant space.