We are going to see the movie Fatal Repulsion. Thereare three parking lots we may park in. One is one block eastof the theater (call this lot 1); one lot is directly behindthe theater (lot 0); and one lot is one block west of thetheater (lot 1). We are approaching the theater from the east.There is an 80% chance that lot 1 will have a vacantspace, a 60% chance that lot 0 will, and an 80% chance thatlot 1 will. Once we pass a lot, we can’t go back to it. Assumethat when we are at a given parking lot, we can determinewhether it has any vacant spaces, but we can’t see any ofthe other lots. Our dates for the evening will assess us apenalty equal to the distance (in blocks) that we park fromthe theater. If we find no space, they will assess a penaltyof 10 (and never go out with us again). What strategyminimizes our expected penalty? Answer the same questionif there is a 70% chance that lot 0 has a vacant space.
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.
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