For 2 events A and B,
(1) Is it true that P(A|B)P(B) = P(B|A)P(A) ? If yes, please provide proof if this is not a law of probability.
(2) Is this still true if A and B are dependent events, not independent events?
Probability
2010-06-01 6:21 pm
回答 (1)
2010-06-01 10:04 pm
✔ 最佳答案
1)Since P(A∩B)=P(B∩A), then P(A|B)P(B)=P(B|A)P(A).
2)
For two independent events A and B, P(A|B)=P(A) and P(B|A)=P(B), P(A|B)P(B) = P(B|A)P(A) is always true.
Also, for two dependent events A and B, P(A|B)P(B)=P(B|A)P(A) is true as well. (From 1)
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