SOLUTION: If I know P(A^B), how do I get P(A^Bcomplement)...where ^ means intersection ....for example P(A) = P(B)_= 1/3 and P(A^B) = to 1/10 What is (a) P(A U Bcomplement) (b) P(

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Question 345519: If I know P(A^B), how do I get P(A^Bcomplement)...where ^ means intersection ....for example
P(A) = P(B)_= 1/3 and P(A^B) = to 1/10
What is (a) P(A U Bcomplement)
(b) P(B^Acomplement)
(c) P(Acomplement U Bcomplement)
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If I know P(A^B), how do I get P(A^Bcomplement)...where ^ means intersection ....
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P(A) + P(A comp) = 1
So, P(A comp) = 1-P(A)
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P(A^B comp) = 1 - P(A^B)
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for example
P(A) = P(B)_= 1/3 and P(A^B) = to 1/10
What is (a) P(A U Bcomplement)
Find P(AUB)
P(AUB) = P(A)+P(B)-P(A^B)
= 1/3 + 1/3 - 1/10
= (2/3)-(1/10)
= (20-3)/30 = 17/30
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The P(AUB comp) = 13/30
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(b) P(B^Acomplement) = P(B-(A^B))
= P(B)-P(A^B)
= P(B)-[P(A)+P(B)-P(AUB)]
= P(AUB)-P(A)
= (17/30)-(1/3)
= 7/30
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(c) P(Acomplement U Bcomplement)
= 1-P(A^B)
= 1-[P(A)+P(B)-P(AUB)]
= 1-[1/3 + 1/3 - (17/30)]
= 1-[(20/30)-(17/30)]
= 1 - 1/10
= 9/10
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Cheers,
Stan H.
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