Question 1141773
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Given P(A)=0.24, P(B)=0.71, and P(A∩B)=0.13, what is P(B∣∣A^c)?
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            Looking into the post,  I think that  the symbol  "||"   (two vertical lines) is a typo,  and it should be 
            only one vertical line instead of twos:


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              Given P(A)=0.24, P(B)=0.71, and P(A∩B)=0.13, what is P(B | A^c)?
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I will solve the problem in this &nbsp;<U>corrected</U> &nbsp;formulation.



<U>Solution</U>


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Use the basic formula (the definition) for the conditional probability


    P(B | A^c) = P(B ∩ A^c) / P(A^c).



We have  P(A^c) = 1 - P(A) = 1 - 0.24 = 0.76.



The set  (B ∩ A^c)  is part of B which does not belong to A, so

    (B ∩ A^c) = B \ (A ∩ B);  therefore,  P(B ∩ A^c) = P(B) - P(A ∩ B) = 0.71 - 0.13 = 0.58.



Thus    P(B | A^c) = P(B ∩ A^c) / P(A^c) = {{{0.58/0.76}}} = 0.7632  (approximately).    <U>ANSWER</U>
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Completed and solved.