document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=266210>Question 266210</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class.\r<BR>\n" );
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document.write( "    (a) What is the probability that the student is both a freshman and an economics major?\r<BR>\n" );
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document.write( "    (b) Given that the student selected is a economics major, what is the probability that she is also an freshman? \r<BR>\n" );
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document.write( "Write your responses as fractions.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195619 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=195619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose that a certain college class contains 65 students. Of these, 36 are freshmen, 34 are economics majors, and 9 are neither. A student is selected at random from the class. <BR>\n" );
document.write( "(a) What is the probability that the student is both a freshman and an economics major?<BR>\n" );
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document.write( "P(frosh and econ) = P(frosh) + P(econ) - P(frosh or econ)<BR>\n" );
document.write( "= 36/65 + 34/65 - (65-9)/65<BR>\n" );
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document.write( "= (36 + 34 - 56)/65<BR>\n" );
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document.write( "= 14/65<BR>\n" );
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document.write( "(b) Given that the student selected is a economics major, what is the probability that she is also an freshman?<BR>\n" );
document.write( "P(frosh|econ) = P(frosh and econ)/P(econ) = (14/65)/(34/65) = 14/34 = 7/17<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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