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OG 12 - Probability

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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by crackthetest » Sat Feb 27, 2010 1:26 pm
On page 118,

" E or F " is the set of outcomes in E or F or both.
" E and F " is the set of outcomes in both E and F.

But P(E or F) = P(E) + P(F) - P(E and F).

I know by additional rule that this is case,
shouldn't "E or F" state " is the set of outcomes in E or F and not both "?
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by kelsi111 » Sun Feb 28, 2010 8:47 am
This comes down to Math talk not exactly mapping to English talk. What you are referring to in
Shouldn't "E or F" state " is the set of outcomes in E or F and not both "?
is called an XOR which is different from OR. I don't know if XOR will be on the GMAT.

OR means that the answer is in either set and doesn't count the middle twice as you would if you just added the two probabilities: P( e OR f ) = P(e) + P(f) - P(e AND f) as you have stated.

An item being in either but not both as you have described is an XOR. P( e XOR f ) = P( e OR f ) - P( e AND f ) = P(e) + P(f) - 2 ( P(e AND f) ).
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