# Is there a function to solve a complicated event probability problem? [closed]

I need to find the probability of this beast: P[(ABEF)+(CDEH)+(ABEI)+(CDEI)+(ABEJ)+(CDEJ)]. A,B,C, etc. represent events with probabilities close to 0.5 so I don't think rare event approximation can be used. The events are not mutually exclusive which is what is giving me difficulties. Is there any way Mathematica can make this easier for me?

## closed as off-topic by Daniel Lichtblau, JimB, gwr, m_goldberg, eyorbleDec 8 '18 at 17:07

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• The short answer is "yes" but I think you're going to have to give a a lot more details. – JimB Dec 6 '18 at 18:58

The following might help. We can take an expression e.g.

expr = (a && b && e && f) || (c && d && e && h);


and express it as an "exclusive sum of products"

BooleanConvert[expr, "ESOP"]
(* (c && d && e && h) ⊻ (a && b && e &&
f && ! h) ⊻ (a && b && ! d && e && f && h) ⊻ (a &&
b && ! c && d && e && f && h) *)


If you can calculate the probabilities of the individual terms, the probability of the expression should simply be the sum of these.