document.write( "Question 367174: what is the probability of (AnB) if P(A) =.50; P(B) =.20; P(A/B) =.75 P(B/A) =.30 P(AuB) =.55 \n" ); document.write( "

Algebra.Com's Answer #261777 by Edwin McCravy(20056) $\"\"$ $\"About$

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what is the probability of (AnB) if P(A) =.50; P(B) =.20; P(A|B) =.75
\n" ); document.write( "P(B|A) =.30 P(AuB) =.55
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document.write( "This gives more information that you need.  So you can do the problem by any of\r\n" );
document.write( "three methods using different ones of those pieces of information.  Here are all\r\n" );
document.write( "three methods:\r\n" );
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document.write( "Method 1:\r\n" );
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document.write( "          P(AnB)  \r\n" );
document.write( "P(A|B) = --------\r\n" );
document.write( "           P(B)\r\n" );
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document.write( "          P(AnB)  \r\n" );
document.write( "  .75 = --------\r\n" );
document.write( "           .20\r\n" );
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document.write( "Multiply both sides by .20\r\n" );
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document.write( "(.20)(.75) = P(AnB)\r\n" );
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document.write( "       .15 = P(AnB)\r\n" );
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document.write( "You only needed P(A|B) and P(B), You did not need either of the other two.\r\n" );
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document.write( "------------------------------\r\n" );
document.write( "Method 2:\r\n" );
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document.write( "          P(BnA)  \r\n" );
document.write( "P(B|A) = --------, ans since BuA and AuB are the same,\r\n" );
document.write( "           P(A)\r\n" );
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document.write( "          P(AnB)  \r\n" );
document.write( "P(B|A) = --------\r\n" );
document.write( "           P(A)\r\n" );
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document.write( "          P(AnB)  \r\n" );
document.write( "  .30 = --------\r\n" );
document.write( "           .50\r\n" );
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document.write( "Multiply both sides by .50\r\n" );
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document.write( "(.50)(.30) = P(AnB)\r\n" );
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document.write( "       .15 = P(AnB)\r\n" );
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document.write( "You only needed P(B|A) and P(A), You did not need either of the other two.\r\n" );
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document.write( "------------------------------\r\n" );
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document.write( "Method 3:\r\n" );
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document.write( "P(AuB) = P(A) + P(B) - P(AnB)\r\n" );
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document.write( "  .55  = .50  + .20  - P(AnB)\r\n" );
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document.write( "  .55  = .70  - P(AnB)\r\n" );
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document.write( "P(AnB) = .15\r\n" );
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document.write( "For this method you only needed P(A), P(B), and P(AuB). You did not need\r\n" );
document.write( "either of the other two.\r\n" );
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document.write( "Edwin

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