αΣfrontierP(b | known, P_1,3, frontier) ΣotherP(P_1,3) P(known) P(frontier) P(other)

P(P_1,3|known, b) = α′P(P_1,3) ΣfrontierP(frontier)

P(P_1,3|known, b) = α′P(P_1,3)

P(P_1,3|known, b) = αΣunknownP(P_1,3, known, b, unknown)

P(¬b|a) = 1 - P(b|a) and we can calculate P(b|a).

We cannot calculate the actual value of P(¬b|a).

P(¬b|a) = P(¬b) - P(a) and we can calculate P(¬b).

P(¬b|a) = P(¬b∧a)/P(a) and we can calculate P(¬b∧a).

αΣfrontierP(b | known, P_1,3, frontier) ΣotherP(P_1,3) P(known) P(frontier) P(other)

P(P_1,3|known, b) = α′P(P_1,3) ΣfrontierP(frontier)

P(P_1,3|known, b) = α′P(P_1,3)

P(P_1,3|known, b) = αΣunknownP(P_1,3, known, b, unknown)

0.016 + 0.064 + 0.144 + 0.576 + 0.108 + 0.012

0.016 + 0.064 + 0.144 + 0.576 + 0.072 + 0.008

0.108 + 0.012 + 0.072 + 0.008 + 0.016 + 0.064

0.108 + 0.012 + 0.072 + 0.008 + 0.016 + 0.144 + 0.576

(0.108 + 0.012) / (0.072 + 0.008 + 0.144 + 0.576)

(0.108

+ 0.012) / (0.108 + 0.012 + 0.016 + 0.064)

(0.072 + 0.008) / (0.072 + 0.008 + 0.144 + 0.576)

(0.072 + 0.008) / (0.108 + 0.012 + 0.016 + 0.064)

P(a ∧ b) = P(a ∧ b)P(b)

P(a ∧ b) = P(a ∨ b)P(b)

(a ∨ b) = P(a | b)P(b)

P(a ∧ b) = P(a | b)P(b)

1/3

1/7

1/8

1/2

1/4

P(cause | effect) = P(cause | effect) P(effect) / P(cause)

P(cause

| effect) = P(effect | cause) P(cause) / P(effect)

P(cause

| effect) = P(cause | effect) P(cause) / P(effect)

P(cause | effect) = P(effect | cause) P(effect) / P(cause)

P(Toothache) P(Weather, Catch, Cavity)

P(Weather) P(Toothache, Catch, Cavity)

P(Cavity) P(Weather, Toothache, Catch)

P(Weather, Toothache) P(Catch, Cavity)

(2)

(3)

None of the given choices

(4)

(1)