document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1012313>Question 1012313</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Krissy wanted to understand whether grade level had any relationship to their opinion on extending the school day. She surveyed some students and displayed the results in the table below:\r<BR>\n" );
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document.write( " 	In favor	Opposed	Undecided<BR>\n" );
document.write( "Grade 9	6	2	7<BR>\n" );
document.write( "Grade 10	5	11	8<BR>\n" );
document.write( "Grade 11	12	15	11<BR>\n" );
document.write( "Grade 12	17	5	13\r<BR>\n" );
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document.write( "Compare P(Grade 11 | opposed) with P(opposed | Grade 11). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #628218 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=628218\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given Table:\r<BR>\n" );
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document.write( "<tr><th></th><th>In Favor</th><th>Opposed</th><th>Undecided</th></tr><tr><th>Grade 9</th><TD >6</TD><TD >2</TD><TD >7</TD></tr><tr><th>Grade 10</th><TD >5</TD><TD >11</TD><TD >8</TD></tr><tr><th>Grade 11</th><TD >12</TD><TD >15</TD><TD >11</TD></tr><tr><th>Grade 12</th><TD >17</TD><TD >5</TD><TD >13</TD></tr>\n" );
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document.write( "Let's add on the totals\r<BR>\n" );
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document.write( "<tr><th></th><th>In Favor</th><th>Opposed</th><th>Undecided</th><th>Total</th></tr><tr><th>Grade 9</th><TD >6</TD><TD >2</TD><TD >7</TD><TD >15</TD></tr><tr><th>Grade 10</th><TD >5</TD><TD >11</TD><TD >8</TD><TD >24</TD></tr><tr><th>Grade 11</th><TD >12</TD><TD >15</TD><TD >11</TD><TD >38</TD></tr><tr><th>Grade 12</th><TD >17</TD><TD >5</TD><TD >13</TD><TD >35</TD></tr><tr><th>Total</th><TD >40</TD><TD >33</TD><TD >39</TD><TD >112</TD></tr>\n" );
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document.write( "The row and column totals are found by adding up the values in each corresponding row or column. For example. The \"15\" in the first row of the column total (far right column) is found by adding up the values in the first row (6+2+7 = 15). The other totals are found the same way. \r<BR>\n" );
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document.write( "Let's first compute <font color=blue>P(Grade 11 | opposed)</font>\r<BR>\n" );
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document.write( "P(Grade 11 | opposed) = (# in grade 11 AND who are opposed)/(# who are opposed)\r<BR>\n" );
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document.write( "P(Grade 11 | opposed) = 15/33\r<BR>\n" );
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document.write( "P(Grade 11 | opposed) = 5/11\r<BR>\n" );
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document.write( "Now let's compute <font color=green>P(Opposed | Grade 11)</font>\r<BR>\n" );
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document.write( "P(Opposed | Grade 11) = (# in grade 11 AND who are opposed)/(# who are in grade 11)\r<BR>\n" );
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document.write( "P(Opposed | Grade 11) = 15/38\r<BR>\n" );
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document.write( "So the two expressions <font color=blue>P(Grade 11 | opposed)</font> and <font color=green>P(Opposed | Grade 11)</font> are NOT the same value (5/11 is not equal to 15/38). This means that the two events <font color=red>being in grade 11</font> and <font color=red>being opposed</font> are NOT independent. The two events are dependent. </SPAN>\n" );
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