Question 1. (100 points) Compute P(P2,2 known, b) in the wumpus world using the formula: P(P2,2 known, b )=P(P2,2)frontierP(b known, P2,2, frontier) P( frontier ) The calculation for P(P1,3 known, b ) is given below. We know the following facts (evidence): b=b1,1b1,2b2,1 known =p1,1p1,2p2,1 P(P1,3 known, b) =P(P1,3)frontierP(b known, P1,3, frontier )P( frontier ) First, compute with P1,3= true: Compute the sum over the frontier: P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)=10.20.2=10.80.2=10.20.8=00.80.8=0.04=0.16=0.16=0.00 The sum is: 0.04+0.16+0.16+0.00=0.36.P(p1,3)=0.2, therefore: P(p1,3)frontierP(b known, p1,3, frontier )P( frontier )=0.20.36=0.072. Then, compute with P1,3= false: Compute the sum over the frontier: P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)P(bknown,p1,3,p2,2,p3,1)P(p2,2,p3,1)=10.20.2=00.80.2=10.20.8=00.80.8=0.04=0.00=0.16=0.00 The sum is: 0.04+0.00+0.16+0.00=0.20.P(p1,3)=0.8, therefore: P(p1,3)frontierP(b known, p1,3, frontier) P( frontier )=0.80.20=0.16. P(P1,3 known, b ===