document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1195976>Question 1195976</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Giving a test to a group of students, the grades and gender are summarized below\r<BR>\n" );
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document.write( "A	B	C	Total<BR>\n" );
document.write( "Male	16	9	19	44<BR>\n" );
document.write( "Female	20	6	7	33<BR>\n" );
document.write( "Total	36	15	26	77\r<BR>\n" );
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document.write( "Write all solutions as a decimals to the fourth. If one student is chosen at random,\r<BR>\n" );
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document.write( "Find the probability that the student got a C: <BR>\n" );
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document.write( "Find the probability that the student was male AND got a \"A\": <BR>\n" );
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document.write( "Find the probability that the student was female OR got an \"C\": <BR>\n" );
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document.write( "If one student is chosen at random, find the probability that the student got a 'A' GIVEN they are male: <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 #828623 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=828623\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given Data Table:<BR>\n" );
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document.write( "<tr><TD ></TD><TD >A</TD><TD >B</TD><TD >C</TD><TD >Total</TD></tr><tr><TD >Male</TD><TD >16</TD><TD >9</TD><TD >19</TD><TD >44</TD></tr><tr><TD >Female</TD><TD >20</TD><TD >6</TD><TD >7</TD><TD >33</TD></tr><tr><TD >Total</TD><TD >36</TD><TD >15</TD><TD >26</TD><TD >77</TD></tr>\n" );
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document.write( "Problem: <font color=blue>Find the probability that the student got a C</font>\r<BR>\n" );
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document.write( "Look at the bottom row labeled \"total\". We have 26 students who got a C out of 77 students in the group.\r<BR>\n" );
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document.write( "Use a calculator to find that<BR>\n" );
document.write( "26/77 = 0.33766233766233<BR>\n" );
document.write( "This value is approximate \r<BR>\n" );
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document.write( "Round this to four decimal places (i.e. nearest ten-thousandth) and you would end up with 0.3377\r<BR>\n" );
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document.write( "Answer: 0.3377\r<BR>\n" );
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document.write( "Problem: <font color=blue>Find the probability that the student was male AND got a \"A\"</font>\r<BR>\n" );
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document.write( "In the \"male\" row, and \"got an A\" column, there are 16 students. <BR>\n" );
document.write( "In short, 16 males got an A.<BR>\n" );
document.write( "This is out of the 77 total in the bottom right corner.\r<BR>\n" );
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document.write( "16/77 = 0.2077922077922 approximately<BR>\n" );
document.write( "This rounds to 0.2078\r<BR>\n" );
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document.write( "Answer: 0.2078\r<BR>\n" );
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document.write( "Problem: <font color=blue>Find the probability that the student was female OR got an \"C\"</font>\r<BR>\n" );
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document.write( "There are 33 female students, 26 students who got a C, and 7 female students who got a C<BR>\n" );
document.write( "33+26-7 = 52 students are female, got a C, or both\r<BR>\n" );
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document.write( "52/77 = 0.67532467532468 = 0.6753<BR>\n" );
document.write( "which is approximate\r<BR>\n" );
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document.write( "Answer: 0.6753\r<BR>\n" );
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document.write( "Problem: <font color=blue>If one student is chosen at random, find the probability that the student got a 'A' GIVEN they are male</font>\r<BR>\n" );
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document.write( "Whenever you see \"given\", it is often a very important key word in probability questions. <BR>\n" );
document.write( "It means that we know 100% that the information provided is correct. This is simply based on the assumption that the speaker is telling the full truth.<BR>\n" );
document.write( "This allows us to narrow our focus. The sample space has been reduced.\r<BR>\n" );
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document.write( "So we are GIVEN the selected student is male. What this means is that we focus entirely on the male row.\r<BR>\n" );
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document.write( "There are 16 males in this row who got an A, out of 44 males total<BR>\n" );
document.write( "16/44 = 0.36363636363637<BR>\n" );
document.write( "16/44 = 0.3636\r<BR>\n" );
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document.write( "Answer:  0.3636<BR>\n" );
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