document.write( "Question 1180354: For two events A and B, P(A) = 0.3 and P(B)=0.2. (a) If A and B are independent, then P(A|B) =
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Algebra.Com's Answer #810029 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Pay no attention to her gripes.

\n" ); document.write( "For two events A and B, P(A) = 0.3 and P(B)=0.2. (a) If A and B are independent, then
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document.write( "Venn diagrams make things easier to understand than formulas alone.\r\n" );
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document.write( "Draw a Venn diagram with sets A and B, with r,s,t,u representing the\r\n" );
document.write( "probabilities of the four regions:\r\n" );
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document.write( "P(A) = 0.3 = r+s\r\n" );
document.write( "P(B) = 0.2 = s+t\r\n" );
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document.write( "Since they are independent,\r\n" );
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document.write( "P(A∩B) = s = P(A)P(B) = (0.3)(0.2) = 0.06    <--ANSWER to P(A∩B)\r\n" );
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document.write( "So since\r\n" );
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document.write( "s = 0.06 and\r\n" );
document.write( "r+s = 0.3, substitution gives\r\n" );
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document.write( "r+0.06 = 0.3\r\n" );
document.write( "r = 0.3-0.06\r\n" );
document.write( "r = 0.24\r\n" );
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document.write( "And since\r\n" );
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document.write( "s = 0.06 and\r\n" );
document.write( "s+t = 0.2\r\n" );
document.write( "0.06+t = 0.2\r\n" );
document.write( "t = 0.14\r\n" );
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document.write( "P(A∪B) = r+s+t = 0.24+0.06+0.14 = 0.44   <--ANSWER to P(A∪B)\r\n" );
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document.write( "Note: We weren't asked for P(A'∩B') = u, but we could have\r\n" );
document.write( "found it because r+s+t+u = 1, so \r\n" );
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document.write( " 0.24+0.06+0.14+u = 1\r\n" );
document.write( "           0.44+u = 1\r\n" );
document.write( "                u = 0.56 \r\n" );
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document.write( "(b) If A and B are dependent and P(A|B) = 0.25,\r\n" );
document.write( "then P(B|A) =\r\n" );
document.write( "P(A∩B) =\r\n" );
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document.write( "P(A|B) = P(A∩B)/P(B) = s/0.2 = 0.25\r\n" );
document.write( "                           s = 0.25(0.2)\r\n" );
document.write( "                           s = 0.05\r\n" );
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document.write( "P(B|A) = P(B∩A)/P(A) = P(A∩B)/P(A) = s/0.2 = 0.05/0.3 = 5/30 = 1/6\r\n" );
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document.write( "(We could have just divided 0.05 by 0.3 and gotten 0.1666666...,\r\n" );
document.write( "but repeating decimals are a hassle, so I multiplied top and bottom\r\n" );
document.write( "by 100 and got the fraction 5/30 which reduced to 1/6.\r\n" );
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document.write( "We aren't asked to, but we could finish out the Venn diagram for (b) if we\r\n" );
document.write( "like:\r\n" );
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document.write( "Edwin
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