Exercise 15.6

Consider the vacuum worlds of Figure vacuum-maze-ch4-figure (perfect sensing) and Figure vacuum-maze-hmm2-figure (noisy sensing). Suppose that the robot receives an observation sequence such that, with perfect sensing, there is exactly one possible location it could be in. Is this location necessarily the most probable location under noisy sensing for sufficiently small noise probability $\epsilon$? Prove your claim or find a counterexample.