Probability question. Since P(E) + P(E') = 1, prove that P(E|F) + P(E'|F) = 1?
回答 (1)
2017-08-28 3:49 pm
Probability question. Since P(E) + P(E') = 1，prove that P(E｜F) + P(E'｜F) = 1?
Sol
P(F｜E)=P(EF)/P(E)
P(EF)=P(E)*P(F｜E)…………
P(F｜E’)=P(E’F)/P(E’)
P(E’F)=P(E’)*P(F｜E)………
P(E｜F)+P(E’｜F)
=P(EF)/P(F)+P(E’F)/P(F)
=P(E)*P(F｜E)/P(F)+P(E’)*P(F｜E)/P(F)
=[P(E)+P(E’)]*P(F｜E)/P(F)
=P(F｜E)/P(F)
=[P(EF)/P(E)]/P(F)
=P(EF)/[P(E)*P(F)]
No
Sol
P(F｜E)=P(EF)/P(E)
P(EF)=P(E)*P(F｜E)…………
P(F｜E’)=P(E’F)/P(E’)
P(E’F)=P(E’)*P(F｜E)………
P(E｜F)+P(E’｜F)
=P(EF)/P(F)+P(E’F)/P(F)
=P(E)*P(F｜E)/P(F)+P(E’)*P(F｜E)/P(F)
=[P(E)+P(E’)]*P(F｜E)/P(F)
=P(F｜E)/P(F)
=[P(EF)/P(E)]/P(F)
=P(EF)/[P(E)*P(F)]
No
收錄日期: 2021-04-30 22:30:06
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170828061832AA1ssl5