document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1176389>Question 1176389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.A survey classified a group of 100 students by sex and according to whether they prefer coco - cola or other brands of soft drink . The proportions falling into the four resulting categories are shown in the accompanying table . ( overline C ) Other brands .14 12 Prefers Sex Coco - Cola ( C ) Boy .44 Girl .30 If a single student is selected from a large group , find the probabilities the events as detailed below : a ) The student is a girl . b ) The student is a boy but does not prefer Coco - Cola c ) The student prefers coco - cola irrespective of Given that the selected student is a girl , what is the probability that she does not prefer Coco - Cola ?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850579 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850579\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this probability problem.\r<BR>\n" );
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document.write( "**Given Information:**\r<BR>\n" );
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document.write( "| Sex  | Coco-Cola (C) | Other Brands (C̄) |<BR>\n" );
document.write( "|------|----------------|-------------------|<BR>\n" );
document.write( "| Boy  | 0.44           | 0.14              |<BR>\n" );
document.write( "| Girl | 0.30           | 0.12              |\r<BR>\n" );
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document.write( "**Total Students:** 100\r<BR>\n" );
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document.write( "**a) The student is a girl.**\r<BR>\n" );
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document.write( "To find the probability of selecting a girl, we add the probabilities of girls preferring Coco-Cola and girls preferring other brands:\r<BR>\n" );
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document.write( "* P(Girl) = P(Girl, C) + P(Girl, C̄)<BR>\n" );
document.write( "* P(Girl) = 0.30 + 0.12<BR>\n" );
document.write( "* P(Girl) = 0.42\r<BR>\n" );
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document.write( "**b) The student is a boy but does not prefer Coco-Cola.**\r<BR>\n" );
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document.write( "This is directly given in the table:\r<BR>\n" );
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document.write( "* P(Boy, C̄) = 0.14\r<BR>\n" );
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document.write( "**c) The student prefers coco-cola irrespective of sex.**\r<BR>\n" );
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document.write( "To find the probability of a student preferring Coco-Cola, we add the probabilities of boys and girls preferring Coco-Cola:\r<BR>\n" );
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document.write( "* P(C) = P(Boy, C) + P(Girl, C)<BR>\n" );
document.write( "* P(C) = 0.44 + 0.30<BR>\n" );
document.write( "* P(C) = 0.74\r<BR>\n" );
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document.write( "**d) Given that the selected student is a girl, what is the probability that she does not prefer Coco-Cola?**\r<BR>\n" );
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document.write( "This is a conditional probability. We want to find P(C̄ | Girl).\r<BR>\n" );
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document.write( "* P(C̄ | Girl) = P(Girl, C̄) / P(Girl)<BR>\n" );
document.write( "* P(C̄ | Girl) = 0.12 / 0.42<BR>\n" );
document.write( "* P(C̄ | Girl) = 12 / 42<BR>\n" );
document.write( "* P(C̄ | Girl) = 2 / 7<BR>\n" );
document.write( "* P(C̄ | Girl) ≈ 0.2857\r<BR>\n" );
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document.write( "**Answers:**\r<BR>\n" );
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document.write( "* **a) P(Girl) = 0.42**<BR>\n" );
document.write( "* **b) P(Boy, C̄) = 0.14**<BR>\n" );
document.write( "* **c) P(C) = 0.74**<BR>\n" );
document.write( "* **d) P(C̄ | Girl) ≈ 0.2857**<BR>\n" );
document.write( " </SPAN>\n" );
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