document.write( "Question 1179151: let M and N be two events, if P(M) =0.12, P(N|M)=0.23, and P(N|M')=0.17, then P(M') = \r
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Algebra.Com's Answer #808712 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "let M and N be two events, if P(M) =0.12, P(N|M)=0.23, and P(N|M')=0.17\r\n" );
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document.write( "This can be done with formulas, but the thinking is easier with a Venn\r\n" );
document.write( "diagram, using reduced sample spaces. [Formulas get you mixed up!]\r\n" );
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document.write( "Let the probabilities of the 4 regions be a,b,c,d.\r\n" );
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document.write( "P(M') = c+d\r\n" );
document.write( "P(M|N) = b/(b+c)\r\n" );
document.write( "P(M'|N) = c/(b+c)\r\n" );
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document.write( "P(M) = 0.12 = a+b\r\n" );
document.write( "P(M') = c+d = 1-P(M) = 1-0.12 = 0.88\r\n" );
document.write( "        c+d = 0.88\r\n" );
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document.write( "P(N|M) = 0.23 = b/(a+b) = b/0.12\r\n" );
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document.write( "        0.23 = b/0.12\r\n" );
document.write( "(0.23)(0.12) = b \r\n" );
document.write( "      0.0276 = b\r\n" );
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document.write( "Substitute in\r\n" );
document.write( "        0.12 = a+b\r\n" );
document.write( "        0.12 = a+0.0276\r\n" );
document.write( "      0.0924 = a\r\n" );
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document.write( "P(N|M') = 0.17 = c/(c+d) = c/0.88\r\n" );
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document.write( "        0.17 = c/0.88\r\n" );
document.write( "(0.17)(0.88) = c\r\n" );
document.write( "      0.1496 = c\r\n" );
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document.write( "Substitute in\r\n" );
document.write( "        c+d = 0.88\r\n" );
document.write( "   0.1496+d = 0.88  \r\n" );
document.write( "          d = 0.7304\r\n" );
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document.write( "P(M|N) = b/(b+c) = 0.0276/(0.0276+0.1496) = 0.0276/0.1772 = 0.1557562077\r\n" );
document.write( "P(M'|N) = c/(b+c) = 0.1496/(0.0276+0.1496) = 0.1496/0.1772 = 0.8442437923\r\n" );
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document.write( "Edwin

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