document.write( "Question 667165: A and B are events defined on a sample space, with P(A) = 0.5 and P(A and B) = 0.2. Find P(B | A). \n" ); document.write( "

Algebra.Com's Answer #414833 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "Formula for conditional probability:\r\n" );
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document.write( "                   P(First AND Second)       P(Second AND First) \r\n" );
document.write( "P(First|Second) = ---------------------  =  ---------------------\r\n" );
document.write( "                       P(Second)                 P(Second)\r\n" );
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document.write( "Note: the events might be in either order on the top since AND \r\n" );
document.write( "is commutative, but the denominator is always the probability \r\n" );
document.write( "of what is given, that is, what is after the vertical line \"|\".\r\n" );
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document.write( "with P(A) = 0.5 and P(A and B) = 0.2. \r\n" );
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document.write( "Find P(B|A)  \r\n" );
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document.write( "Here the First = B and the Second = A\r\n" );
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document.write( "                   P(Second AND First) \r\n" );
document.write( "P(First|Second) = ---------------------\r\n" );
document.write( "                       P(Second)\r\n" );
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document.write( "           P(A and B)     0.2\r\n" );
document.write( "P(B|A) = ------------- = ----- =   = 0.4\r\n" );
document.write( "              P(A)        0.5\r\n" );
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document.write( "Edwin

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