In our analysis of the wumpus world, we used the fact that each square contains a pit with probability 0.2, independently of the contents of the other squares. Suppose instead that exactly N/5 pits are scattered uniformly at random among the N squares other than [1, 1]. Are the variables P and P i, j and P k, l still independent? What is the joint distribution P (P1, 1..., P4, 4) now? Redo the calculation for the probabilities of pits in [1.3] and [2.2].