document.write( "Question 1160040: P(A) = 0.5
\n" ); document.write( "P(B) = 0.8
\n" ); document.write( "P(A ᑎ B ) = 0.3
\n" ); document.write( "Solve this question
\n" ); document.write( "1. P ( A|A ᑎ B)
\n" ); document.write( "2. P ( A ᑎ B | A ᑌ B ) \n" ); document.write( "

Algebra.Com's Answer #783213 by Edwin McCravy(20086) $\"\"$ $\"About$

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P( A ) = 0.5
\n" ); document.write( "P( B ) = 0.8
\n" ); document.write( "P( A ᑎ B ) = 0.3
\n" ); document.write( "Solve this question
\n" ); document.write( "1. P ( A | A ᑎ B )
\n" ); document.write( "2. P ( A ᑎ B | A ᑌ B )
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document.write( "The formula for conditional probability is\r\n" );
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document.write( "             P( X ᑎ Y )              \r\n" );
document.write( "P( X | Y ) = ————————————\r\n" );
document.write( "               P( Y )\r\n" );
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document.write( "1. P ( A | A ᑎ B )\r\n" );
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document.write( "Substitute A for X and A ᑎ B for Y\r\n" );
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document.write( "                  P[ A ᑎ (A ᑎ B) ]    P[ (A ᑎ A) ᑎ B ]    P( A ᑎ B )      \r\n" );
document.write( "P ( A | A ᑎ B ) = ————————————————— = ————————————————— =  ——————————— = 1\r\n" );
document.write( "                     P( A ᑎ B )          P( A ᑎ B )        P( A ᑎ B )\r\n" );
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document.write( "It is certain that you are given A if you are given A and B.\r\n" );
document.write( "It doesn't even matter what the probabilities for A, B are.\r\n" );
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document.write( "2. P ( A ᑎ B | A ᑌ B )\r\n" );
document.write( "\r\n" );
document.write( "Substitute A ᑎ B for X and A ᑌ B for Y\r\n" );
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document.write( "                      P[(A ᑎ B) ᑎ (A ᑌ B) ]              \r\n" );
document.write( "P( A ᑎ B | A ᑌ B ) = ——————————————————————\r\n" );
document.write( "                           P( A ᑌ B )\r\n" );
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document.write( "We simplify \r\n" );
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document.write( "(A ᑎ B) ᑎ (A ᑌ B) = [(A ᑎ B) ᑎ A] ᑌ [(A ᑎ B) ᑎ B] =\r\n" );
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document.write( "[A ᑎ (B ᑎ A)] ᑌ [A ᑎ (B ᑎ B)] = [A ᑎ (A ᑎ B)] ᑌ (A ᑎ B) =\r\n" );
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document.write( "[(A ᑎ A) ᑎ B)] ᑌ (A ᑎ B) = (A ᑎ B) ᑌ (A ᑎ B) = A ᑎ B\r\n" );
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document.write( "The formula for\r\n" );
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document.write( "P( X ᑌ Y ) = P( X ) + P( Y ) - P( X ᑎ Y ) \r\n" );
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document.write( "P( A ᑌ B ) = P( A ) + P( B ) - P( A ᑎ B )\r\n" );
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document.write( "P( A ᑌ B ) = 0.5 + 0.8 - 0.3 = 1\r\n" );
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document.write( "                       P( A ᑎ B )     0.3            \r\n" );
document.write( "P( A ᑎ B | A ᑌ B ) = ————————————— = ———— = 0.3\r\n" );
document.write( "                       P( A ᑌ B )      1     \r\n" );
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document.write( "Edwin

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