Question 470498: This is the question: For 2 events A and B defined on a sample space S,
N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2. Given that
N(S)= 120, how many outcomes belong to neither A Nor B?
This is a sample space and algebra of sets problem. I'm not sure where to start.
Thanks.
Found 2 solutions by stanbon, robertb:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! For 2 events A and B defined on a sample space S,
N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2. Given that
N(S)= 120, how many outcomes belong to neither A Nor B?
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Draw 2 intersecting circles; label them A and B.
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Draw a rectangle around the circles ; label it S=120
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Put "2" in the intersection of A and B.
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Put "15" in the part of A that is not in the intersection.
Put "50" in the part of B that is not in the intersection.
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Now you see there are 15+2+50 = 67 in A or B.
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Therefore there are 120 - 67 = 53 in S that are not in A or B.
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Cheers,
Stan H.
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Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! N(A) = N((A and B') U (A and B)) = N(A and B') + N(A and B) = 15 + 2 = 17
N(B) = N((A' and B) U (A and B)) = N(A' and B) + N(A and B) = 50 + 2 = 52
==> N( A U B) = N(A) + N(B) - N(A and B) = 17 + 52 - 2 = 67
==> N((A U B)') = N(S) - N(A U B) = 120 - 67 = 53.
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