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?
put on hold as off-topic by Daniel Lichtblau, JimB, gwr, m_goldberg, eyorble Dec 8 at 17:07
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – Daniel Lichtblau, m_goldberg, eyorble
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.