YLL討論網

以S表示S=T, ~S表示S=F.  對R,C同.
重寫題目條件
p(C)=0.5,      p(~C)=0.5
p(S|C)=0.1,    p(~S|C)=0.9
p(S|~C)=0.5,  p(~S|~C)=0.5
p(R|C)=0.8,    p(~R|C)=0.2
p(R|~C)=0.2,   p(~R|~C)=0.8
p(w|S&R)=0.99
p(w|~S&R)=0.9
p(w|S&~R)=0.9
p(w|~S&~R)=0

問p(C|S&R)=?

解題
p(S&C)= p(S|C)* p(C)=0.1*0.5=0.05
p(S)= p(S|C)* p(C)+ p(S|~C)* p(~C)= 0.1*0.5+0.5*0.5=0.3
p(~S)=0.7
p(S&C)= p(C|S)* p(S),  0.05=0.3*p(C|S)
p(C|S)=1/6

p(R&C)= p(R|C)* p(C)=0.8*0.5=0.4
p(R)= p(R|C)* p(C)+ p(R|~C)* p(~C)= 0.8*0.5+0.2*0.5=0.5
p(~R)=0.5
p(R&C)= p(C|R)* p(R),  0.4=0.5*p(C|R)
p(C|R)=0.8

p(C&S&R)=p(C|S&R)*p(S&R)
---

似乎條件不足, 在此私自加一假設:
設S|C和R|C獨立, 也就是說
p(S&R|C)= p(S|C)* p(R|C)

則得下表
C     p(S&R)     p(S&~R)     p(~S&R)     p(~S&~R)
T     0.08     0.02     0.72     0.18
F     0.1     0.4     0.1     0.4


p(S&R&C)= p(S&R|C)* p(C)=0.08*0.5=0.04
p(S&R)= p(S&R|C)* p(C)+ p(S&R|~C)* p(~C)= 0.04+0.1*0.5=0.09

p(C&S&R)=p(C|S&R)*p(S&R)
0.04= p(C|S&R)*0.09
p(C|S&R)=4/9