3. In this question, we want to practice probabilistic reasoning in the Wumpus world shown in Fig. 3. For the Wumpus world, we assume that an agent has explored the locations: [1,1],[1,2] and [2,1]. We also assume that the agent observed a breeze at [1,2] and [2,1]. The breeze is felt adjacent to the squares with pits. Each square can independently have a pit with 0.8 probability (therefore no pit with probability 0.2 ). We want to decide the query: which location is better between [1,3] and [2,2] ? In order to solve the query, we define two random variables pW and bW:pWJ is true if and only if the location [i,j] contains a pit, b1, is true if and only if [i,j] is breezy. Consider p1,1,,p,A and b2,1,b1,2,b2,1 only. Further, we define two more randomyariables: known =p1,1p1,2p2,1 and b=b1,1b1,2 b2,1. If we group 'unknown' pits into 'frontier (or fringe)' and 'other' like the Fig.4, we can express P(p1,3) known, b) as P(p1,3) fringe P(b known, p1,3 fringe )P( fringe ) as shown in the following Fig 5. P(P1,3 known, b)=unknounP(P1,3, unknown, knowen, b) line 1 =unknownP(bP1,3. known, unknown )P(P1,3, known, unknown ) line 2 =fringeother(bknown,P1,3 fringe, other )P(P1,3 known, fringe, other ) line 3 =afringeotherP(b known, P1,3, fringe )P(P1,3,known, fringe, other ) line 4 =fringeP(b known, P1,3 fringe )otherP(P1,3, known, fringe, other ) line 5 =afringeP(b known, P1,3, fringe )otherP(P1,3)P( known )P (fringe) P (other ) line 6 =P( known )P(P1,3)fringeP(b known, P1,3, fringe )P( fringe )otherP( other ) line 7 =P(P1,3)rrinarP(b known, P1,3 fringe )P( fringe ) (1) How can we proceed to the line 3 from the line 2 ? (Please answer briefly by considering the relation between 'unknown' and 'fringe' and 'other') (3pts) (2) How can we proceed to the line 5 from the line 4 ? (3pts) (3) How can we proceed to the line 8 from the line 7? (3pts)