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Logics and probability

• To: mathgroup at smc.vnet.net
• Subject: [mg78475] Logics and probability
• From: "Dr. Wolfgang Hintze" <weh at snafu.de>
• Date: Mon, 2 Jul 2007 07:00:32 -0400 (EDT)
• Reply-to: "Dr. Wolfgang Hintze" <weh at snafu.de>

Hello,

this is really a very elementary question.
How can I treat the logics and numerics of probabilities?

For example consider two events A and B.

The probability of the event (A U B) is then

w1 = P(A U B) = P(A) + P(B) - P(A/\B)

Now let P(A) = P(B) = p and P(A/\B) = p^2 then

w1 = p(2-p).

When we have to deal with more complicated expressions like

w2 = P((AB/\BD) U (AB/\BC/\CB) U (AC/\BC/\BD) U (AC/\CD))

where there are five events AB, BD, BC, CD, AC.

How can Mathematica calculate the probability for me?
Some kind of "ProbabilityExpand" should reduce the expression
to a sum of probablities of pure AND-events (LogicExpand is not 
appropriate).

Thanks in advance
Wolfgang

• Follow-Ups:
  • Re: Logics and probability
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>