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Importance of Having Sample Space Defined
An innocent questionhas been posted to theMathematics group on
Facebook:
Hi, I'm an amateur so I'm sorry if this is something well known
and
uninteresting. Is 1 + 1 = 1 in probability theory?:
Consider tossing a coin and throwing a dice. Let the set of all
possible
outcomes for the coin be C. which implies p(C) = 1. Let the set
of all
possible outcomes for the dice be D, which implies p(D) = 1. Now
p(CD)
which is the probability that either the events D or C occur is
also 1.
Here's the interesting bit: C and D are disjoint setsand
therefore
p(CD)= p(C) + P(D) which implies 1 = 1 + 1.
But then I started having doubts because I made some
unproved
assumptions such as p(C) and p(D) and so on, are actually
defined in such
a situation as this and whether C and D are truly disjoint.
Help!
How would you respond to this appeal?
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2/17/2014 Importance of Having Sample Space Defined
http://www.cut-the-knot.org/Probability/SampleSpacesImportance.shtml
Probability Paradoxes
Bertrand's Paradox
Monty Hall dilemma
Parrondo Paradox
Symmetry Principle in Probability
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Copyright 1996-2014Alexander Bogomolny
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CITE THIS PAGE AS:A. Bogo moln y, Importan ce of Havin g Samp le
Sp ace Defin edfrom Interactive Mathematics Miscellany and
Puzzles
http://www.cut-the-knot.org/Probability/SampleSpacesImportance.shtml,
Accessed 17 February 2014
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