document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194945>Question 1194945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem about Compound Events:(union, intersection and complement):\r<BR>\n" );
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document.write( "Of 500 college students, 115 are enrolled in math, 205 are enrolled in English, and 45 are enrolled in both. If a student is selected at random, find the probability of the following. (See Example 5. Round your answers to three decimal places.)<BR>\n" );
document.write( "(a) The student is enrolled in mathematics.\r<BR>\n" );
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document.write( "(b) The student is enrolled in English.\r<BR>\n" );
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document.write( "(c) The student is enrolled in both.\r<BR>\n" );
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document.write( "(d) The student is enrolled in mathematics or English.\r<BR>\n" );
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document.write( "(e) The student is enrolled in English but not in mathematics.\r<BR>\n" );
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document.write( "(f) The student is not enrolled in English or is enrolled in mathematics.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #827238 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52786)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=827238\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Please help me solve this word problem about Compound Events:(union, intersection and complement):<BR>\n" );
document.write( "Of 500 college students, 115 are enrolled in math, 205 are enrolled in English, and 45 are enrolled in both. <BR>\n" );
document.write( "If a student is selected at random, find the probability of the following. <BR>\n" );
document.write( "(See Example 5. Round your answers to three decimal places.)<BR>\n" );
document.write( "(a) The student is enrolled in mathematics.\r<BR>\n" );
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document.write( "(b) The student is enrolled in English.\r<BR>\n" );
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document.write( "(c) The student is enrolled in both.\r<BR>\n" );
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document.write( "(d) The student is enrolled in mathematics or English.\r<BR>\n" );
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document.write( "(e) The student is enrolled in English but not in mathematics.\r<BR>\n" );
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document.write( "(f) The student is not enrolled in English or is enrolled in mathematics.<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "(a)  P(M) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=115%2F500 ALIGN=MIDDLE  ALT=\"115%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "         First, it is obvious and does not require further explanation.\r\n" );
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document.write( "         I intently left it without reducing the fraction, to make logic and expression clear to you.\r\n" );
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document.write( "         You may reduce it on your own.\r\n" );
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document.write( "(b)  P(E) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=205%2F500 ALIGN=MIDDLE  ALT=\"205%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "         Again, it is obvious and does not require further explanation.\r\n" );
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document.write( "         I intently left it without reducing the fraction, to make logic and expression clear to you.\r\n" );
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document.write( "         You may reduce it on your own.\r\n" );
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document.write( "(c)  P(M and E) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F500 ALIGN=MIDDLE  ALT=\"45%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "         Again, it is obvious, because it is given that 45 students are enrolled in both.\r\n" );
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document.write( "         I intently left it without reducing the fraction, to make logic and expression clear to you.\r\n" );
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document.write( "         You may reduce it on your own.\r\n" );
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document.write( "(d)  P(M or E) = use the formula for the UNION of events, which is = P(M) + P(E) - P(M and E).\r\n" );
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document.write( "         Each of the three terms in the right side is just calculated above in (a), (b) and (c). So you simply\r\n" );
document.write( "         substitute the relevant values in this formula\r\n" );
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document.write( "             P(M or E) = P(M) + P(E) - P(M and E) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=115%2F500 ALIGN=MIDDLE  ALT=\"115%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=205%2F500 ALIGN=MIDDLE  ALT=\"205%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F500 ALIGN=MIDDLE  ALT=\"45%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "         Calculate and then reduce the fraction on your own.\r\n" );
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document.write( "(e)  P(E but not M) = P(E) - P(M and E).\r\n" );
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document.write( "         Simply from P(E) subtract P(M and E).\r\n" );
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document.write( "         Wording explanation is that you want that part of E which is not (M and E).\r\n" );
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document.write( "         Again, you just know P(E) from (b) and know  P(M and E) from (c),\r\n" );
document.write( "         so all you need is to substitute those values into the formula\r\n" );
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document.write( "             P(E but not M) = P(E) - P(M and E) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=205%2F500 ALIGN=MIDDLE  ALT=\"205%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=45%2F500 ALIGN=MIDDLE  ALT=\"45%2F500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r\n" );
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document.write( "         Calculate and then reduce the fraction on your own.\r\n" );
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document.write( "(f)  Regarding (f), it is too MUCH questions for one post,\r\n" );
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document.write( "     so and THEREFORE I do not go into further explanations.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;My rule is &nbsp;DO &nbsp;NOT &nbsp;PACK &nbsp;too much in one post, &nbsp;since otherwise the student's brain does not process it.  <BR>\n" );
document.write( "     &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It requires and deserves a &nbsp;SEPARATE &nbsp;post.\r<BR>\n" );
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document.write( "At this point, &nbsp;I complete my explanations.\r<BR>\n" );
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document.write( "Please let me know if you do understand everything and every point from the outlined explanations.\r<BR>\n" );
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document.write( "////////////////\r<BR>\n" );
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document.write( "To see many other similar &nbsp;(and different) &nbsp;solved problems, &nbsp;look into the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-operations-on-sets-help-solving-Probability-problems.lesson>Elementary operations on sets help solving Probability problems</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Probability-and-statistics/Elementary-operations-on-sets-help-solving-Probability-problems-REVISITED.lesson>Elementary operations on sets help solving Probability problems - REVISITED</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in &nbsp;ALGEBRA-II &nbsp;in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Solved problems on Probability</U>\". \r<BR>\n" );
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document.write( "Save the link to this textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in ALGEBRA-II<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r<BR>\n" );
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document.write( "into your archive and use when it is needed.\r<BR>\n" );
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document.write( "Consider these lessons as your textbook,  &nbsp;handbook,  &nbsp;a Solutions Manual, &nbsp;tutorials and &nbsp;(free of charge)  &nbsp;home teacher.\r<BR>\n" );
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document.write( "Happy learning (!)\r<BR>\n" );
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