document.write( "Question 1160923: Given p(B)=0.5 and p(AuB')=0.8. What is the value of p(A/B)?
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Algebra.Com's Answer #784560 by ikleyn(52794) $\"\"$ $\"About$

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document.write( "Note that the complement to  (A U B')  is  (A' ∩ B).\r\n" );
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document.write( "Therefore, P(A' ∩ B) = 1 - P(A U B') = 1 - 0.8 = 0.2.\r\n" );
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document.write( "Next,        (A' ∩ B) U  (A ∩ B) = B,  and the sets  (A' ∩ B) and  (A ∩ B)  are disjoint.\r\n" );
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document.write( "Therefore,  P(A' ∩ B) + P(A ∩ B) = P(B),   or\r\n" );
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document.write( "              0.2     + P(A ∩ B) = 0.5,\r\n" );
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document.write( "which implies  P(A ∩ B) = 0.5 - 0.2 = 0.3.\r\n" );
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document.write( "Hence, by the definition of the conditional probability, \r\n" );
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document.write( "           P(A | B) = P(A ∩ B) / P(B) =  = 0.6.    ANSWER\r\n" );
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