Hi all, Just to confirm: is it true that P(!A|B)=1-P(A|B) ? but is it not true that P(A|!B)=1-P(A|B)? where ! means not ie !A is "not A" or are neither of these true? i have assumed these results from solutions of questions that i have done, but want to check that i am right thanks
For a little context: april 2014 Q3 part b) we find P(A!|AE) by 1-P(A|AE) but Sep 2013 Q7 part ii) we are finding P(Claim | !C) and using 1-P(Claim|C) does not give correct answer
The first equation holds (perhaps have a go at proving it). The second doesn’t, e.g. say we’re rolling a dice, and A is ”lands on 1” and B is ”lands on an even number”. Then P{A|B}+P{A|!B}=0+1/3=1/3.
