document.write( "Question 855471: if P(B)=0,2 P(A\B)=0,7 P(B')=0,8 AND P(A\B')=0,9 FIND P(B\A) \n" ); document.write( "
Algebra.Com's Answer #515392 by Edwin McCravy(20060)\"\" \"About 
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document.write( " P(B)=0.2 P(A|B)=0.7 P(B')=0.8 AND P(A|B')=0.9 FIND P(B|A)\r\n" );
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document.write( "Let P(A&B')=w, P(A&B)=x, P(A'&B)=y, P(A'&B')=z, \r\n" );
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document.write( "then \r\n" );
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document.write( "(1)   w+x+y+z=1\r\n" );
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document.write( "(2)   P(B)= x+y = 0.2\r\n" );
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document.write( "(3)   P(A|B) = x/(x+y) = 0.7\r\n" );
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document.write( "(4)   P(B') = w+z = 0.8\r\n" );
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document.write( "(5)   P(A|B') = (w+x)/(w+z) = 0.9\r\n" );
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document.write( "From (1) and (2), \r\n" );
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document.write( "(6)  w+z = 0.8 \r\n" );
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document.write( "From (2) and (3),\r\n" );
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document.write( "\"system%28x%2By=0.2%2Cx%2F%28x%2By%29=0.7%29\" get \r\n" );
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document.write( "(7)  x=0.14\r\n" );
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document.write( "(8)  y=.06\r\n" );
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document.write( "From (4) and (5)\r\n" );
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document.write( "(9)  w+x = 0.72\r\n" );
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document.write( "from (7) and (9)\r\n" );
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document.write( "(10) w = 0.58\r\n" );
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document.write( "From (6) and (10)\r\n" );
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document.write( "(11) z = 0.22 \r\n" );
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document.write( "P(B|A) = x/(x+w) = 0.14/(0.14+0.58) = 0.14/0.72 = 14/72 = 7/36\r\n" );
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document.write( "Edwin
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