Re: How to calculate a union
- To: mathgroup at smc.vnet.net
- Subject: [mg104536] Re: How to calculate a union
- From: rat <b at fas.com>
- Date: Tue, 3 Nov 2009 02:55:31 -0500 (EST)
- References: <hcjjdv$jte$1@smc.vnet.net> <hcl3rn$buv$1@smc.vnet.net>
Helen Read: > Bill Rowe wrote: >> On 10/31/09 at 1:54 AM, ramiro.barrantes at gmail.com (Ramiro) wrote: >> >>> I am trying to compute the probability of a union, the formula >>> requires to sum and subtract all possible combinations of >>> intersections for all pairs, triplets, etc. When n is big, getting >>> all the terms is a challenge. Otherwise, I can easily compute any >>> given intersection. >>> ex. P(AUBUC) = P(A) + P(B) + P(C) - (P(A,B)+P(A,C)+P(B,C)) + >>> P(A,B,C) >> Hmm... You say you are computing a probability. So, I would read >> P(AUBUC) as being the probability of event A or event B or event >> C occurring. Using that interpretation then >> >> P(AUBUC) = P(A) + P(B) + P(C) >> >> where I've assumed events A,B and C are independent events. > > The size union is only equal to the sum of the sizes of the individual > sets if the sets are disjoint, which one cannot assume. > >> This is clearly different than the expression you have. >> Additionally, P(A,B) is meaningless to me. > > He meant P(A intersect B) by that, and has applied the > inclusion/exclusion principle correctly. > > Hi Helen. I have a similar problem. I'm new to Mathematica and I'd like to program the inclusion-exclusion principle to calculate P(AUBUCUD), for different probabilities P(A),P(B),P(C),P(D) asuming these events are indepedent. What functions would be useful? I need something to start investigating...
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