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# Union of three sets formula derivation?

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Joined: 31 Dec 1969
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Kudos [?]: 232 [0], given: 104556

Union of three sets formula derivation? [#permalink]

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10 Jan 2012, 18:20
okay so i know the formula for this is:
P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + P(AnBnC)
but i literally do not understand how to get the P(AnBnC)
can someone please beak it down for me ?
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Re: Union of three sets formula derivation? [#permalink]

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10 Jan 2012, 20:10
1
KUDOS
Expert's post
Let's suppose an object X is in A, B, and C.

Since you are counting A, B, and C serparately, you've counted X three times.

But then, you subtract everything in A & B, B & C, and A & C. X is in each of those, so you've subtracted X three times. That means you haven't actually counted X.

So, you need to add X (and every other object in A, B, and C) to get the correct total, because otherwise you aren't counting it.
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Re: Union of three sets formula derivation?   [#permalink] 10 Jan 2012, 20:10
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