       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>

```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.

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