document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199934>Question 1199934</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For Biological Science and Education faculties combined, 1/6 of the female and 1/4 of the male faculty members are associate professors. If a person is randomly chosen from these two departments, what is the probability that a faculty member is an associate professor?<BR>\n" );
document.write( "       || BS  || Education || Social Sciences || Total ||<BR>\n" );
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document.write( "Male   || 10  ||   26      ||  19             ||  55   ||<BR>\n" );
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document.write( "Female || 15  ||   21      ||  17             ||  53   ||<BR>\n" );
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document.write( "Total  || 25  ||   47      ||  36             ||  108  ||<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 #833924 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=833924\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
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document.write( "<tr><TD ></TD><TD >Biological Science</TD><TD >Education</TD><TD >Social Sciences</TD><TD >Total</TD></tr><tr><TD >Male</TD><TD >10</TD><TD >26</TD><TD >19</TD><TD >55</TD></tr><tr><TD >Female</TD><TD >15</TD><TD >21</TD><TD >17</TD><TD >53</TD></tr><tr><TD >Total</TD><TD >25</TD><TD >47</TD><TD >36</TD><TD >108 </TD></tr>\n" );
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document.write( "15 female faculty members in Biological Science.<BR>\n" );
document.write( "21 female faculty members in Education.<BR>\n" );
document.write( "15+21 = 36 total female faculty members from either field.<BR>\n" );
document.write( "1/6 of 36 = 6 female associate professors in Biological Science and Education combined.\r<BR>\n" );
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document.write( "10 male faculty members in Biological Science.<BR>\n" );
document.write( "26 male faculty members in Education.<BR>\n" );
document.write( "10+26 = 36 total male faculty members from either field.<BR>\n" );
document.write( "1/4 of 36 = 9 male associate professors in Biological Science and Education combined.\r<BR>\n" );
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document.write( "6 female + 9 male = 15 total associate professors from the two fields mentioned.<BR>\n" );
document.write( "Let A = 15 so we can use it later.\r<BR>\n" );
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document.write( "There are 25 faculty members from Biological Science and 47 from Education.<BR>\n" );
document.write( "That gives 25+47 = 72 total faculty members.<BR>\n" );
document.write( "Let B = 72.<BR>\n" );
document.write( "We ignore the social sciences entirely because of the phrasing \"a person is randomly chosen from these two departments\", and those two departments are of course Biological Science and Education.\r<BR>\n" );
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document.write( "We have A = 15 faculty members who are associate professors in either of the two fields mentioned. <BR>\n" );
document.write( "This is out of B = 72 faculty members total from these two fields. \r<BR>\n" );
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document.write( "Divide A over B<BR>\n" );
document.write( "A/B = 15/72 = (3*5)/(3*24) = 5/24\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>5/24</font><BR>\n" );
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