Re: How to calculate a union
- To: mathgroup at smc.vnet.net
- Subject: [mg104505] Re: How to calculate a union
- From: Helen Read <hpr at together.net>
- Date: Sun, 1 Nov 2009 17:58:31 -0500 (EST)
- References: <hcjjdv$jte$1@smc.vnet.net>
- Reply-to: HPR <read at math.uvm.edu>
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. -- Helen Read Mathematics & Statistics University of Vermont