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17 Sep 2015, 22:55
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Hi,
In one of the GMAT preparation notes, the following was stated :-
1) "E or F" is the set of outcomes in E or F or both, that is E U F
2) P(E or F) = P(E) + P(F) - P( E and F)
However i don't understand why the formula is deducting the probability of E & F because if they deduct that then the statement "both" in item 1 will become untrue.
If E or F = E or F or both, then how can they deduct the "both" from the summation of E + F?
I think the correct formula should be E or F = P(E) + P(F)
Can someone explain this?
In one of the GMAT preparation notes, the following was stated :-
1) "E or F" is the set of outcomes in E or F or both, that is E U F
2) P(E or F) = P(E) + P(F) - P( E and F)
However i don't understand why the formula is deducting the probability of E & F because if they deduct that then the statement "both" in item 1 will become untrue.
If E or F = E or F or both, then how can they deduct the "both" from the summation of E + F?
I think the correct formula should be E or F = P(E) + P(F)
Can someone explain this?
19 Sep 2015, 22:37
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rajak01,
This is an extension of the set theory where the number of elements that are in set A or B is given by:
n(A or B) = n(A) + n(B) - n(A and B)
So if there are 20 students taking French and 30 students taking Spanish and there are 10 students taking Spanish and French, then the number of students taking French or Spanish is given by 20+30-10=40. You are subtracting the overlap. The same idea then extends to probability of selecting a member from a particular set. I am explaining it in very simple terms, but that is the basic idea.
Dabral
This is an extension of the set theory where the number of elements that are in set A or B is given by:
n(A or B) = n(A) + n(B) - n(A and B)
So if there are 20 students taking French and 30 students taking Spanish and there are 10 students taking Spanish and French, then the number of students taking French or Spanish is given by 20+30-10=40. You are subtracting the overlap. The same idea then extends to probability of selecting a member from a particular set. I am explaining it in very simple terms, but that is the basic idea.
Dabral
20 Sep 2015, 19:01
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dabral
Hi Debral,
Thanks for replying. However, please refer to the statement 1 which is stated as :- "E or F" is the set of outcomes in E or F or both, that is E U F
Hence the way i interpret this statement is E U F is E alone + F alone and inclusive of the intersection both.
Therefore if we use this formula P(E or F) = P(E) + P(F) - P( E and F) this will mean that E alone + F alone but excluding both because the intersection has been deducted.
Hence the word "both" in this statement must be excluded if we were to use the above formula :- "E or F" is the set of outcomes in E or F or both, that is E U F
