if
since
thus
rearranging the equation gives you
As for question two here a hint
Can anyone give help with this proof question.
The question states:
Let A and B be events with 0 < P(A) < 1 and 0 < P(B) < 1. B is said to favor A if P(A|B) > P(A).
(i) Show that if B favours A, then A also favours B, i.e. if P(A|B) > P(A) then P(B|A) > P(B).
(ii) Show that if B favours A, then B complement favours A complement, i.e. show that if P(A|B) > P(A) then P(A complement | B complement) > P(A complement).