       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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