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not to be republished
PROBABILITY      543
Definition 2 Two events E and F are said to be independent, if
P(F|E) = P (F)  provided P (E)  ≠ 0
and
P (E|F) = P (E)  provided P (F)  ≠ 0
Thus, in this definition we need to have P (E) ≠ 0 and  P(F) ≠ 0
Now, by the multiplication rule of probability, we have
P(E ∩ F) = P(E) P (F|E) (1)
If E and F are independent, then (1) becomes
P(E ∩ F) = P(E) P(F)