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# Probability theory

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Manager
Joined: 11 Aug 2012
Posts: 127
Schools: HBS '16, Stanford '16

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18 Jan 2013, 07:37
1
KUDOS
In probability questions, specifically OR problems (addition problems), the formula is:

P(A or B) = P(A) + P(B) - P(A AND B)

Why do we have to substract P(A AND B)?, I think we do that because P(A) and P(B) already include P(A AND B), right?

VP
Joined: 23 Mar 2011
Posts: 1113
Concentration: Healthcare, Strategy
Schools: Duke '16 (M)

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18 Jan 2013, 08:39
danzig wrote:
In probability questions, specifically OR problems (addition problems), the formula is:

P(A or B) = P(A) + P(B) - P(A AND B)

Why do we have to substract P(A AND B)?, I think we do that because P(A) and P(B) already include P(A AND B), right?

correct.
p(a) and p(b) both include p(a & b). so essentially when you want to write p(a or b), you mean p(only a)+p(only b)+p(a&b). ---1

where as, p(a)+p(b)= [p(only a)+ p(a&b)] + [p(only b)+p(a&b)]

hence you want to subtract p(a&b) from p(a)+p(b) to obtain equation #1.

Hope its clear. You should also try making a Venn diagram; that shall make this a bit more easier.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

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21 Jan 2013, 06:04
danzig wrote:
In probability questions, specifically OR problems (addition problems), the formula is:

P(A or B) = P(A) + P(B) - P(A AND B)

Why do we have to substract P(A AND B)?, I think we do that because P(A) and P(B) already include P(A AND B), right?

Yes, it is the same as the sets concept:

n(A or B) = n(A) + n(B) - n(A and B)

n(A) and n(B) both include n(A and B). You cannot double count it so you must subtract it once. Check out this sets post to see how it is represented in the venn diagram:
http://www.veritasprep.com/blog/2012/09 ... s-of-sets/

If you need to find the probability of 'A or B but not both', you will need to subtract P(A and B) twice.

P(A or B but not both) = P(A) + P(B) - 2*P(A and B)
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Re: Probability theory   [#permalink] 21 Jan 2013, 06:04
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