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My textbook states that two events E and F are independent if any one of the following conditions are met: (i) P(E/F)= P(E) (ii)P(F/E)=P(F) (iii)P(E n F)=P(E).P(F)

Is it correct to then assume that if E and F are independent having met condition (i) or (ii), then E and F are also mutually exclusive?

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    $\begingroup$ No -- in fact, mutually exclusive is an incredibly strong form of DEPENDENCE: if one happens, then you know for a fact that the other didn't. $\endgroup$ – Nick Peterson Apr 4 '17 at 18:05
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No. Mutually exclusive or disjoint if they cannot both be true.

$P(E|F) = \frac{P(E \cap F)}{P(F)}$

As independent event $P(E \cap F) = P(E)\cdot P(F)$

$= \frac{P(E)\cdot P(F)}{P(F)}$

$= P(E)$

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