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Union of three sets formula derivation?

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Joined: 31 Dec 1969

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Location: Russian Federation
Concentration: Entrepreneurship, International Business
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)
Union of three sets formula derivation? [#permalink]

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New post 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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New post 10 Jan 2012, 20:10
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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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Kudos [?]: 296 [1], given: 2

Re: Union of three sets formula derivation?   [#permalink] 10 Jan 2012, 20:10
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Union of three sets formula derivation?

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