SOLUTION: 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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Question 1141773: Given P(A)=0.24, P(B)=0.71, and P(A∩B)=0.13, what is P(B∣∣A^c)?
Answer by ikleyn(52852)   (Show Source): You can put this solution on YOUR website!
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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: 

              Given P(A)=0.24, P(B)=0.71, and P(A∩B)=0.13, what is P(B | A^c)?

            I will solve the problem in this  corrected  formulation.


Solution 

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) =  = 0.7632  (approximately).    ANSWER

Completed and solved.



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