document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=515540>Question 515540</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If P(A or B) = 0.5, P(A) = 0.2 and P(B) = 0.7, determine<BR>\n" );
document.write( "P(A and B).<BR>\n" );
document.write( "  (Points : 3)<BR>\n" );
document.write( "       0.10<BR>\n" );
document.write( "       0.35  <BR>\n" );
document.write( "       0.40<BR>\n" );
document.write( "       0.90<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344050 by </B><A HREF=/tutors/aboutme.mpl?userid=drcole><B>drcole(72)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drcole><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=344050\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The inclusion-exclusion principle tells us that:\r<BR>\n" );
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document.write( "P(A or B) = P(A) + P(B) - P(A and B)\r<BR>\n" );
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document.write( "We subtract P(A and B) because A and B is included in both A and B, so by just taking P(A) + P(B), you are double-counting the overlap P(A and B).\r<BR>\n" );
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document.write( "We know that P(A or B) = 0.5, P(A) = 0.2, and P(B) = 0.7.  We substitute these values into the formula above and solve for P(A and B).\r<BR>\n" );
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document.write( "0.5 = 0.2 + 0.7 - P(A and B)<BR>\n" );
document.write( "0.5 = 0.9 - P(A and B) (simplify)<BR>\n" );
document.write( "-0.4 = -P(A and B) (subtract 0.9 from both sides)<BR>\n" );
document.write( "0.4 = P(A and B) (negate both sides)\r<BR>\n" );
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document.write( "So P(A and B) = 0.4. </SPAN>\n" );
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