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Mutually Exclusive versus Independent Events-ECO6416

# Mutually Exclusive versus Independent Events-ECO6416 - If...

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Mutually Exclusive versus Independent Events Mutually Exclusive (ME): Event A and B are ME if both cannot occur simultaneously. That is, P[A and B] = 0. Independency (Ind.): Events A and B are independent if having the information that B already occurred does not change the probability that A will occur. That is P[A given B occurred] = P[A]. If two events are ME they are also Dependent: P(A given B) = P[A and B] ÷ P[B], and since P[A and B] = 0 (by ME), then P[A given B] = 0. Similarly, If two events are Independent then they are also not ME.
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Unformatted text preview: If two events are Dependent then they may or may not be ME. If two events are not ME, then they may or may not be Independent. The following Figure contains all possibilities. The notations used in this table are as follows: X means does not imply, question mark ? means it may or may not imply, while the check mark means it implies. Notice that the (probabilistic) pairwise independency and mutual independency for a collection of events A 1 ,..., A n are two different notions....
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