Wikipedia:Reference desk/Archives/Mathematics/2015 May 19

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May 19

Probability question

According to Bayes theorem P(B|A)=P(A|B)*P(B)/P(A). But using the same theory, I can't work out why P(B'|A')=P(B')+P(A|B')*P(B')/P(A'). There is obviously another rule which has been used here but which rule is it? — Preceding unsigned comment added by 94.0.242.23 (talk) 01:33, 19 May 2015 (UTC)

P(B'|A')=P(B')+P(A|B')*P(B')/P(A') is not true in general i.e.without additional constraints on the events. To see that choose A=B'^c (complement of B'), in which case P(A|B') = 0 and your relation reduces to P(B'|A')=P(B'), which obviously doesn't hold in general. Abecedare (talk) 02:13, 19 May 2015 (UTC)