document.write( "Question 1089593: If A and B are events in the same space such that P(A)=0.7, P(B)=0.2, and P(A∩B)=0.1, compute P(A∩B)¯. [input a number, e.g. 0.123] \n" ); document.write( "
Algebra.Com's Answer #704305 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!

\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Let w,x,y, and z be the probabilities of those regions in\r\n" );
document.write( "the Venn diagram. \r\n" );
document.write( "\r\n" );
document.write( "Then \r\n" );
document.write( "\r\n" );
document.write( "P(A) = 0.7 = w + x\r\n" );
document.write( "P(B) = 0.2 = x + y\r\n" );
document.write( "P(A∩B) = 0.1 = x\r\n" );
document.write( "P(AUBUCUD) = 1 = w + x + y + z\r\n" );
document.write( "\r\n" );
document.write( "Substituting 0.1 for x from P(A∩B) = 0.1 = x\r\n" );
document.write( "\r\n" );
document.write( "P(A) = 0.7 = w + 0.1\r\n" );
document.write( "P(B) = 0.2 = 0.1 + y\r\n" );
document.write( "P(AUBUCUD) = 1 = w + 0.1 + y + z\r\n" );
document.write( "\r\n" );
document.write( "0.7 = w + 0.1        0.2 = 0.1 + y\r\n" );
document.write( "0.6 = w              0.1 = y\r\n" );
document.write( "\r\n" );
document.write( "Substituting those:\r\n" );
document.write( "\r\n" );
document.write( "P(AUBUCUD) = 1 = 0.6 + 0.1 + 0.1 + z\r\n" );
document.write( "\r\n" );
document.write( "  1 = 0.6 + 0.1 + 0.1 + z\r\n" );
document.write( "  1 = 0.8 + z\r\n" );
document.write( "0.2 = z\r\n" );
document.write( "\r\n" );
document.write( "So the Venn diagram is now:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "That's the Venn diagram.\r\n" );
document.write( "\r\n" );
document.write( "I don't know what you mean by  P(A∩B)¯. I've never seen that\r\n" );
document.write( "line up there before.\r\n" );
document.write( "\r\n" );
document.write( "Is it the complement of P(A∩B)?  If so, all we needed to do was\r\n" );
document.write( "subtract P(A∩B) from 1 or 1 - 0.1 = 0.9.  But surely they wouldn't \r\n" );
document.write( "have given you all that other un-needed information if that was all \r\n" );
document.write( "they wanted.  If you know what regions you wanted just add up the \r\n" );
document.write( "probabilities in those regions.\r\n" );
document.write( "\r\n" );
document.write( "If you like, you can explain what you mean by P(A∩B)¯ in the \r\n" );
document.write( "thank-you note form below and I'll get back to you by email.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );