If E and F are events in S (sample space) the the conditional probability of E and F is P(E|F) = P(E intersect F).
Further :
the conditional probability of "E" given "F" is =$ \frac {P(EnF)}{P(F)} $
defn: if P(E|F) = P(E) , then E and F are independent events otherwise they are dependant events.
note: independence implies that $ P(E)= P(E|F) = \frac {P(EnF)}{P(F)} $
or P(E).P(F)=P(EnF).
note : if P(E|F) = P(E)
then P(F|E) = P(F)
