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)
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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
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由 大嘴 於 星期一 四月 10, 2006 7:29 pm
[問題]求救,機率問題
由 enesn 於 星期五 四月 07, 2006 7:07 pm
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