document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=113276>Question 113276</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780321386724/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> In a group of 100 students, 30 are HIstory majors, 6 of the History majors have a dual major in Business, in addition there are 45 Business majors, and there are 25 Engineering majors (none of which have dual majors and no student has a triple major. Many students have not declared a major. Determine the probability that a a student selected at random is either a business or engineering major.\r<BR>\n" );
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document.write( "***I am confused because I have a total of 100 students and some how I am coming up with a 51% probability that a random student selected is eiher business or engineering; however, I am not taking into consideration those who are NOT declared majors. How far off am I? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #82430 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=82430\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a relatively straight-forward counting problem, but you have to be careful not to count someone twice.\r<BR>\n" );
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document.write( "First thing is that there are 30 History majors, but 6 of them are dual History/Business majors, that means that there are only 30 - 6 = 24 students that are ONLY History majors.  Likewise, of the 45 Business majors, 6 of them are dual, so 45 - 6 = 39 are ONLY Business.\r<BR>\n" );
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document.write( "In summary:\r<BR>\n" );
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document.write( "24 Only History<BR>\n" );
document.write( "39 Only Business<BR>\n" );
document.write( "6 History/Business<BR>\n" );
document.write( "25 Engineering\r<BR>\n" );
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document.write( "All of that totals to 94, but there are 100 students, so that means 6 students have no major at all.\r<BR>\n" );
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document.write( "The business majors in the random selection could be either from the Business only group or the dual History/Business group, so that is a total of 45, plus there are 25 Engineering majors, making a total of 70 possibilities out of the 100 students.  Therefore the desired probability is 0.70.\r<BR>\n" );
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document.write( "As an aid to having this make sense, consider this:  The only way a student from this group could NOT be either an Engineering or Business major is if the student were a History ONLY major or had not selected his major yet.  There are 24 History only and 6 no major students for a total of 30, so there is a 0.30 probability that the student is NOT either Engineering or Business, or 1 - the probability that the student is from either of those two groups.\r<BR>\n" );
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document.write( "Hope this helps<BR>\n" );
document.write( "John </SPAN>\n" );
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