document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=470498>Question 470498</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is the question: For 2 events A and B defined on a sample space S, <BR>\n" );
document.write( "N(AandBcomplement)= 15, N(Acomplement and B)= 50, and N(A and B)=2.  Given that <BR>\n" );
document.write( "N(S)= 120, how many outcomes belong to neither A Nor B?<BR>\n" );
document.write( "This is a sample space and algebra of sets problem.  I'm not sure where to start.<BR>\n" );
document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322707 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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/cgi-bin/show-face.mpl?user=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> N(A) = N((A and B') U (A and B)) = N(A and B') + N(A and B) = 15 + 2 = 17\r<BR>\n" );
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document.write( "N(B) = N((A' and B) U (A and B)) = N(A' and B) + N(A and B) = 50 + 2 = 52\r<BR>\n" );
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document.write( "==> N( A U B) = N(A) + N(B) - N(A and B) = 17 + 52 - 2 = 67\r<BR>\n" );
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document.write( "==> N((A U B)') = N(S) - N(A U B) = 120 - 67 = 53. </SPAN>\n" );
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