Independent and Mutually Exclusive Events

Question

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?

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. — Nick Peterson, Apr 04 '17 at 18:05
Does this answer your question? Independent and mutually exclusive — , Dec 24 '21 at 08:57

score 0 · Answer 1 · answered Apr 04 '17 at 18:07

0

No. Mutually exclusive or disjoint if they cannot both be true.

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

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

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

$= P(E)$

answered Apr 04 '17 at 18:07

Kanwaljit Singh

8,610

Independent and Mutually Exclusive Events

1 Answers1