document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=659042>Question 659042</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a scientific study there are 14 guinea pigs, 9 of which are pregnant. If 3 are selected at random without replacement, find the probability that none are pregnant. Enter your answer as a fraction or as a number rounded to three decimal places. Correct answer: 5/182\r<BR>\n" );
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document.write( "I have the answer, but cannot figure out to get that fraction - Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #410609 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=410609\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 9 out of 14 guinea pigs are pregnant for a probability of 9/14.<BR>\n" );
document.write( "3 are selected at random without replacement.<BR>\n" );
document.write( "what is the probability that none are pregnant.<BR>\n" );
document.write( "probability of a guinea pig being pregnant is 9/14.<BR>\n" );
document.write( "probability of a guinea pig not being pregnant is 5/14.<BR>\n" );
document.write( "the probability of the first guinea pig not being pregnant is 5/14.<BR>\n" );
document.write( "the probability of the second guinea pig not being pregnant is 4/13.<BR>\n" );
document.write( "the probability of the third guinea pig not being pregnant is 3/12.<BR>\n" );
document.write( "the probability of all 3 not being pregnant is 5/14 * 4/13 * 3/12<BR>\n" );
document.write( "this can be simplified to 5/14 * 4/13 * 1/4 which can be further simplified to 5/14 * 1/13 which is equal to 5/(14*13) which is equal to 5/182.<BR>\n" );
document.write( "the alternate way of looking at is finding the probability by finding the number of ways you can get all non-pregnant women and dividing that by the number of ways you can get any women.<BR>\n" );
document.write( "the formula for the number of ways to get 3 non-pregnant women out of a pool of 5 non-pregnant women is C(5,3) which is equal to 10.<BR>\n" );
document.write( "the formula for the number of ways to get 3 women out of a pool of 14 women is C(14,3) which is equal to 364.<BR>\n" );
document.write( "the probability is 10 / 364 which simplifies to 5/182.<BR>\n" );
document.write( "pick the method you feel most comfortable with and go with that.\r<BR>\n" );
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