Conditional Probability true or false question?

For any two events X and Y, P(X | Y) = 1 - P(Y |X).





true or false?Conditional Probability true or false question?
Let's see... the probability of X given Y is true = 1 - the probability of Y given X is true? That would be FALSE.





Counterexample:





There are are 100 people in a room. Fifty are doctors, and of those 25 are women. There are only 25 women in the room (the 50 non-doctors are all men.) In that case:





P(Woman | Doctor) = 25/50 = 0.5 = 50%


P(Doctor | Woman) = 25/25 = 1.0 = 100%Conditional Probability true or false question?
This is false; however, the following statement is true:





P(X/Y)=1-P( notX /Y)