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February 11th, 2011, 12:07 PM   #1
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Statistics Homework

If I have three events, A,B and C, and I want the event that only A will occur, would the formula be this?

P(A n B' n C')= P(A)- P(A n B) - P(A n C) - P(A n B n C)

When I do it, I keep getting a negative number, -1.03, and the answer is suppose to be 0.03.

P(A) = 0.70
P(B)= 0.8
P(C) = 0.75

P(A u B) = 085
P(A u C)= 0.90
P(B u C)= 0.95
P(A u B u C)= 0.98
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February 11th, 2011, 12:33 PM   #2
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Re: Statistics Homework

Your formula uses intersections like P(A n B) but then you list unions P(A u B), P(A u C), etc. What values did you get for the intersections?



Look at the Venn diagram. You subtracted P(A n B n C) three times: once when you subtracted P(A n B), once when you subtracted P(A n C), and once again at the end. The formula should end +P(A n B n C), not -P(A n B n C). This is an example of the "inclusion-exclusion principle".
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February 11th, 2011, 12:43 PM   #3
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Re: Statistics Homework

Oh, I am sorry for the confusion. Those values I posted were the given values for the question.

I am still confused though. Why would it be plus at the end? If I wanted to find the event of only A occurring, wouldn't I subtract those three intersection for the probability of A?
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February 11th, 2011, 01:07 PM   #4
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Re: Statistics Homework

The problem is that P(A n B n C) is part of P(A n B). So when you took away P(A n B) you took away P(A n B n C) as well. Unfortunately the diagram I posted doesn't make that clear.
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February 13th, 2011, 12:30 PM   #5
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Re: Statistics Homework

Oh, okay! I thought that P(A n B) was completely separate from P(A n B n C). Thank you!
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