2. 2

3. 3

4. 5.5.1
Theorem) n
X = (T1 = x1 )∧(T2 = x2 )∧· · ·∧(Tn = xn )
CH X C = {C1 , C2 , ...}
X CH
X CH 5.3
P (CH ∩ X) P (X | CH )P (CH )
P (CH | X) =
CH =
(C = )
P (X) P (X)
P (CH |A) A
P (CH |X)
5.4
P (CH ∩ X) = P (CH | X)P (X) = PP (C| CHX) (CH ) 4 H )
(X H ∩ )P P (X|C

5. P (CH ∩ X) P (X | CH )P (CH )
P (CH | X) = =
P (X) P (X)

6. P (C = | X) > P (C = × | X)
P (C = | X) < P (C = × | X)
6

7. P (X | C )P (C )
P (C | X) =
P (X)
P (C ) = N /N
X = (T1 = x1 ) ∧ (T2 = x2 ) ∧ · · · ∧ (Tn = xn )
= x1 ∧ x2 ∧ · · · ∧ x3
P (X | C ) = P (x1 ∧ x2 ∧ · · · ∧ xn | C )
= P (x1 | C )P (x2 | C ) · · · P (xn | C )
n
= P (xk | C )
k=1
P (X) CH

8. P (C ) = 4/10 = 0.4, P (C× ) = 6/10 = 0.6
X = (T1 = No) ∧ (T2 = No) ∧ (T3 = Yes) ∧ (T4 = Yes)
8

9. X = (T1 = No) ∧ (T2 = No) ∧ (T3 = Yes) ∧ (T4 = Yes)
P (X | C ) = P (T1 = No | C ) × P (T2 = No | C )
×P (T3 = Yes) | C ) × P (T4 = Yes | C )
P (T1 = No | C ) = 2/4 = 0.5
P (T2 = No | C ) = 0/4 = 0.0
P (T3 = Yes | C ) = 2/4 = 0.5
P (T4 = Yes | C ) = 0/4 = 0.0
P (X|C ) = 0.5 × 0.0 × 0.5 × 0.0 = 0.0
P (X | C ) · P (C ) = 0.0 × 0.4 = 0.0

10. X = (T1 = No) ∧ (T2 = No) ∧ (T3 = Yes) ∧ (T4 = Yes)
P (X | C× ) = P (T1 = No | C× ) × P (T2 = No | C× )×
P (T3 = Yes | C× ) × P (T4 = Yes | C× )
P (T1 = No | C× ) = 4/6 = 0.667
P (T2 = No | C× ) = 4/6 = 0.667
P (T3 = Yes | C× ) = 1/6 = 0.167
P (T4 = Yes | C× ) = 4/6 = 0.667
P (X|C× ) = 0.667 × 0.667 × 0.167 × 0.667 = 0.0494
P (X | C× ) · P (C× ) = 0.0494 × 0.4 = 0.0198

11. P (X | C ) · P (C ) = 0.0
P (X | C× ) · P (C× ) = 0.0198
P (X | C ) · P (C ) < (X | C× ) · P (C× )
11

12. 12