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 #827236 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=827236\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "M = event of selecting a student in math<BR>\n" );
document.write( "P(M) = probability of selecting a math student<BR>\n" );
document.write( "P(M) = (number of math students)/(number total)<BR>\n" );
document.write( "P(M) = 115/500<BR>\n" );
document.write( "P(M) = 0.23\r<BR>\n" );
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document.write( "Answer: <font color = red>0.23</font>\r<BR>\n" );
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document.write( "Part (b)\r<BR>\n" );
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document.write( "E = event of selecting a student in English<BR>\n" );
document.write( "P(E) = probability of selecting an English student<BR>\n" );
document.write( "P(E) = (number of English students)/(number total)<BR>\n" );
document.write( "P(E) = 205/500<BR>\n" );
document.write( "P(E) = 0.41\r<BR>\n" );
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document.write( "Answer: <font color = red>0.41</font>\r<BR>\n" );
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document.write( "Part (c)\r<BR>\n" );
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document.write( "E and M = event of selecting student in both classes<BR>\n" );
document.write( "P(E and M) = (number in both)/(number total)<BR>\n" );
document.write( "P(E and M) = 45/500<BR>\n" );
document.write( "P(E and M) = 0.09\r<BR>\n" );
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document.write( "Answer: <font color = red>0.09</font>\r<BR>\n" );
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document.write( "Part (d)\r<BR>\n" );
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document.write( "E or M = event of selecting a student in either class (or both)\r<BR>\n" );
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document.write( "n(E or M) = number of students in either class or both<BR>\n" );
document.write( "n(E or M) = n(E) + n(M) - n(E and M)<BR>\n" );
document.write( "n(E or M) = 205 + 115 - 45<BR>\n" );
document.write( "n(E or M) = 275\r<BR>\n" );
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document.write( "P(E or M) = n(E or M)/(number total)<BR>\n" );
document.write( "P(E or M) = 275/500<BR>\n" );
document.write( "P(E or M) = 0.55\r<BR>\n" );
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document.write( "Answer: <font color = red>0.55</font>\r<BR>\n" );
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document.write( "Part (e)\r<BR>\n" );
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document.write( "n(E) = number in English class = 205<BR>\n" );
document.write( "n(E and M) = number in both classes = 45\r<BR>\n" );
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document.write( "n(E not M) = number in English, but not math<BR>\n" );
document.write( "n(E not M) = n(E) - n(E and M)<BR>\n" );
document.write( "n(E not M) = 205 - 45<BR>\n" );
document.write( "n(E not M) = 160\r<BR>\n" );
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document.write( "P(E not M) = n(E not M)/(500 total)<BR>\n" );
document.write( "P(E not M) = 160/500<BR>\n" );
document.write( "P(E not M) = 0.32\r<BR>\n" );
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document.write( "Answer: <font color = red>0.32</font>\r<BR>\n" );
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document.write( "Part (f)\r<BR>\n" );
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document.write( "I interpret this to mean \"find the probability of someone that isn't in either class\". Let me know if your teacher meant something else.\r<BR>\n" );
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document.write( "500 total students<BR>\n" );
document.write( "n(E or M) = 275 in either class<BR>\n" );
document.write( "n(not E and not M) = 500 - n(E or M)<BR>\n" );
document.write( "n(not E and not M) = 500 - 275<BR>\n" );
document.write( "n(not E and not M) = 225 students in neither class\r<BR>\n" );
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document.write( "225/500 = 0.45 is the probability of selecting a student that is not in English, and also not in Math either.\r<BR>\n" );
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document.write( "Answer: <font color = red>0.45</font><BR>\n" );
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