document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201039>Question 1201039</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At a liberal arts college in the Midwest, 39% of freshman are enrolled in both a math course and an English course, 11% are enrolled in a math course, but not an English course, and 63% are enrolled in an English course. What is the probability that a freshman student selected at random is taking an English course but not a mathematics course? What is the probability a student is not enrolled in either course?   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835296 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=835296\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "This is one way to have a starting Venn Diagram template.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C-2%2C10%2C-2%2C8%2C%0D%0Aline%281%2C1%2C1%2C6%29%2Cline%281%2C6%2C8%2C6%29%2Cline%288%2C6%2C8%2C1%29%2Cline%288%2C1%2C1%2C1%29%2C%0D%0A%0D%0Acircle%283.64%2C3.44%2C2%29%2Ccircle%285.64%2C+3.44%2C2%29%2C%0D%0A%0D%0Alocate%287.2%2C8%2Cmatrix%281%2C3%2C%22M%22%2C%22=%22%2C%22math%22%29%29%2C%0D%0Alocate%287.2%2C7.5%2Cmatrix%281%2C3%2C%22E%22%2C%22=%22%2C%22English%22%29%29%2C%0D%0A%0D%0Alocate%281.84%2C5.34%2CM%29%2C%0D%0Alocate%286.76%2C5.82%2CE%29%2C%0D%0Alocate%282.6%2C4%2Ca%29%2C%0D%0Alocate%284.38%2C4%2Cb%29%2C%0D%0Alocate%286.26%2C4.24%2Cc%29%2C%0D%0Alocate%286.9%2C1.82%2Cd%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "M = set of freshmen taking math (some also taking English)<BR>\n" );
document.write( "E = set of freshmen taking English (some also taking math)<BR>\n" );
document.write( "region a = freshmen taking math only<BR>\n" );
document.write( "region b = freshmen taking both math and English<BR>\n" );
document.write( "region c = freshmen taking English only<BR>\n" );
document.write( "region d = freshmen taking neither course\r<BR>\n" );
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document.write( "Let's say there are 1000 freshmen as a hypothetical situation.\r<BR>\n" );
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document.write( "Given facts<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "<tr><TD >Number</TD><TD >Statement</TD></tr><tr><TD >1</TD><TD >39% of freshmen are enrolled in </br>both a math course and an English course</TD></tr><tr><TD >2</TD><TD >11% are enrolled in a math course, </br>but not an English course</TD></tr><tr><TD >3</TD><TD >63% are enrolled in an English course</TD></tr>\n" );
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document.write( "Fact 1 means there are 0.39*1000 = 390 freshmen enrolled in both math and English. <BR>\n" );
document.write( "This value will replace \"b\" in the Venn Diagram above.\r<BR>\n" );
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document.write( "Fact 2 means there are 0.11*1000 = 110 freshmen enrolled in math, but not in English. <BR>\n" );
document.write( "This value will replace \"a\" in the Venn Diagram above.\r<BR>\n" );
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document.write( "Fact 3 means there are 0.63*1000 = 630 freshmen enrolled in English (some of these students may also be in math). <BR>\n" );
document.write( "Subtract off the amount of freshmen taking both to get 630-390 = 240. <BR>\n" );
document.write( "This is the number of freshmen taking English only.<BR>\n" );
document.write( "This value replaces the \"c\" in the Venn Diagram above.\r<BR>\n" );
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document.write( "This is what you should have so far.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C-2%2C10%2C-2%2C8%2C%0D%0Aline%281%2C1%2C1%2C6%29%2Cline%281%2C6%2C8%2C6%29%2Cline%288%2C6%2C8%2C1%29%2Cline%288%2C1%2C1%2C1%29%2C%0D%0A%0D%0Acircle%283.64%2C3.44%2C2%29%2Ccircle%285.64%2C+3.44%2C2%29%2C%0D%0A%0D%0Alocate%287.2%2C8%2Cmatrix%281%2C3%2C%22M%22%2C%22=%22%2C%22math%22%29%29%2C%0D%0Alocate%287.2%2C7.5%2Cmatrix%281%2C3%2C%22E%22%2C%22=%22%2C%22English%22%29%29%2C%0D%0A%0D%0Alocate%28-1%2C8%2Cmatrix%281%2C2%2C%22Hypothetical%22%2C%22Scenario%3A%22%29%29%2C%0D%0Alocate%28-1%2C7.5%2Cmatrix%281%2C3%2C%221000%22%2C%22freshmen%22%2C%22total%22%29%29%2C%0D%0A%0D%0Alocate%281.84%2C5.34%2CM%29%2C%0D%0Alocate%286.76%2C5.82%2CE%29%2C%0D%0Alocate%282.6%2C4%2C110%29%2C%0D%0Alocate%284.38%2C4%2C390%29%2C%0D%0Alocate%286.26%2C4.24%2C240%29%2C%0D%0Alocate%286.9%2C1.82%2Cd%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The a,b,c was replaced with 110, 390, and 240 in that exact order.<BR>\n" );
document.write( "The amount of freshmen so far is 110+390+240 = 740\r<BR>\n" );
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document.write( "Since there are 1000 freshmen total, we know that 1000-740 = 260 freshmen aren't taking math and aren't English either. <BR>\n" );
document.write( "This value will replace \"d\" in the diagram.\r<BR>\n" );
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document.write( "Here's the final Venn Diagram<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28400%2C300%2C-2%2C10%2C-2%2C8%2C%0D%0Aline%281%2C1%2C1%2C6%29%2Cline%281%2C6%2C8%2C6%29%2Cline%288%2C6%2C8%2C1%29%2Cline%288%2C1%2C1%2C1%29%2C%0D%0A%0D%0Acircle%283.64%2C3.44%2C2%29%2Ccircle%285.64%2C+3.44%2C2%29%2C%0D%0A%0D%0Alocate%287.2%2C8%2Cmatrix%281%2C3%2C%22M%22%2C%22=%22%2C%22math%22%29%29%2C%0D%0Alocate%287.2%2C7.5%2Cmatrix%281%2C3%2C%22E%22%2C%22=%22%2C%22English%22%29%29%2C%0D%0A%0D%0Alocate%28-1%2C8%2Cmatrix%281%2C2%2C%22Hypothetical%22%2C%22Scenario%3A%22%29%29%2C%0D%0Alocate%28-1%2C7.5%2Cmatrix%281%2C3%2C%221000%22%2C%22freshmen%22%2C%22total%22%29%29%2C%0D%0A%0D%0Alocate%281.84%2C5.34%2CM%29%2C%0D%0Alocate%286.76%2C5.82%2CE%29%2C%0D%0Alocate%282.6%2C4%2C110%29%2C%0D%0Alocate%284.38%2C4%2C390%29%2C%0D%0Alocate%286.26%2C4.24%2C240%29%2C%0D%0Alocate%286.9%2C1.82%2C260%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "As a check:<BR>\n" );
document.write( "a+b+c+d = 110+390+240+260 = 1000\r<BR>\n" );
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document.write( "=============================================================\r<BR>\n" );
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document.write( "Now to answer the questions.\r<BR>\n" );
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document.write( "Problem 1) <font color=blue>What is the probability that a freshman student selected at random is taking an English course but not a mathematics course?</font>\r<BR>\n" );
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document.write( "Refer to the Venn Diagram above.<BR>\n" );
document.write( "We see there are 240 freshmen taking English but not math. <BR>\n" );
document.write( "This is out of 1000 freshmen total.<BR>\n" );
document.write( "240/1000 = 0.24\r<BR>\n" );
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document.write( "Answer: <font color=red>0.24</font>\r<BR>\n" );
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document.write( "------------------------------------\r<BR>\n" );
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document.write( "Problem 2) <font color=blue>What is the probability a student is not enrolled in either course?</font>\r<BR>\n" );
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document.write( "Refer to the Venn Diagram above.<BR>\n" );
document.write( "There are 260 freshmen that aren't taking either course mentioned. <BR>\n" );
document.write( "This is out of 1000 freshmen total.\r<BR>\n" );
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document.write( "260/1000 = 0.26\r<BR>\n" );
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document.write( "Answer: <font color=red>0.24</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );