QUESTION THREE $(3)$

$($a$)$ Three missionaries and three cannibals are on one side of a river, along with a boat that

can hold one or two people. Find a way to get everyone to the other side, without ever

leaving a group of missionaries outnumbered by cannibals.

$($i$)$ Write the problem formulation for the task above?

$[1$ Marks$]$

$($ii$)$ Solve the problem using the problem formulation?

$[2$ Marks$]$

$($iii$)$ Which of the following statements are true given the Bayesian network

below? For false statements, show one active trail.

$P(H,J)=P(H|J)P(J)$

$P(H,J|L)=P(H|L)P(J|L)$

$P(C,I|F)=P(C|F)P(I|F)$

$P(C,I|G,A)=P(C|G,I)P(I|G,A)$

$P(A,D|B)=P(A|B)P(D|B)$

$P(B,F)=P(B)P(F)$

P$($C$,$K$|$B$,$F$)=$P$($C$|$B$,$F$)$P$($K$|$B$,$F$)$

P$($E$,$K$|$L$)=$P$($B$)$P$($K$|$L$)$