document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=361410>Question 361410</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a class of 50 students, 31 are democrats, 13 are business majors, and 3 of the business majors are democrats.  If one student is randomly selected from the class, find the probability of choosing a Democrat or business major. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257702 by </B><A HREF=/tutors/aboutme.mpl?userid=neatmath><B>neatmath(302)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=neatmath><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=neatmath><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=257702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 50 students total. <br>\r<BR>\n" );
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document.write( "Now we need to find out how many students fit our parameters of Democrat or business major.<br>\r<BR>\n" );
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document.write( "There are 31 Democrats, and 13 business majors.  However, 3 of the business majors are ALSO Democrats.<br>\r<BR>\n" );
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document.write( "So here are the totals we really have for Democrats and business majors:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=31%2B13-3=41 ALIGN=MIDDLE  ALT=\"31%2B13-3=41\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Thus, the probability of choosing a Democrat or business major is just:<br>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41%2F50 ALIGN=MIDDLE  ALT=\"41%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<br>\r<BR>\n" );
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document.write( "0.82<br>\r<BR>\n" );
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document.write( "Therefore, P(Democrat or business major)=0.82<br>\r<BR>\n" );
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document.write( "We could also use the formula P(A or B) = P(A) + P(B) - P(A and B) to calculate this.  <br>\r<BR>\n" );
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document.write( "This is likely how your instructor would like you to solve this problem, see below:<br>\r<BR>\n" );
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document.write( "P(D or B)=P(D)+P(B)-P(D and B)<br>\r<BR>\n" );
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document.write( "P(D or B)=31/50+13/50-3/50<br>\r<BR>\n" );
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document.write( "P(D or B)=41/50=0.82 which agrees with our probability above!<br>\r<BR>\n" );
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document.write( "I hope this helps!<br> </SPAN>\n" );
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