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Discussion: Roundtable
Topic: Mutually Exclusive and Complementary Events


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Subject:   RE: Mutually Exclusive and Complementary Events
Author: Craig
Date: Oct 28 2004
As I was out running this morning, I thought of another way to describe the
difference between mutually exclusive/complementary and independence...

ME/C refers to different values a random variable can have, while
independent/dependent can refer to either different random variables or to
different trials.

For example, in the just-concluded World Series, "Boston wins the game" and
"St. Louis wins the game" are complementary events that are values that the
random variable, "winner of the game" can take on.  "Where the game is played"
can be thought of as a random variable (if you think of choosing one of the
games at random), and the values that this random variable could take on are
"Boston" and "St. Louis."  In this World Series, the two random variables "who
wins the game" and "where the game is played" are independent (since the
probability of St. Louis having won a game chosen at random is zero!!!).  But
these might not be independent in another World Series, where "home team
advantage" might be a factor.

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