document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205230>Question 1205230</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following table lists the joint probabilities associated with smoking and lung disease among 60-to-65 year-old men.\r<BR>\n" );
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document.write( "|||||||||||||||||||smoker||||non smoker<BR>\n" );
document.write( "Has lung diseas::::0.1||||||||0.03<BR>\n" );
document.write( "No lung disease::::0.16|||||||0.71\r<BR>\n" );
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document.write( "One 60-to-65 year old man is selected at random. What is the probability of the following events?\r<BR>\n" );
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document.write( "A. He is a smoker: \r<BR>\n" );
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document.write( "B. He does not have lung disease: \r<BR>\n" );
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document.write( "C. He has lung disease given that he is a smoker: \r<BR>\n" );
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document.write( "D. He has lung disease given that he does not smoke </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842184 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=842184\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Given table<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Smoker</TD><TD >Nonsmoker</TD></tr><tr><TD >Lung Disease</TD><TD >0.1</TD><TD >0.03</TD></tr><tr><TD >No Lung Disease</TD><TD >0.16</TD><TD >0.71</TD></tr>\n" );
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document.write( "I'll multiply each of those values in the table by 100<BR>\n" );
document.write( "Eg: 0.1*100 = 10<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Smoker</TD><TD >Nonsmoker</TD></tr><tr><TD >Lung Disease</TD><TD >10</TD><TD >3</TD></tr><tr><TD >No Lung Disease</TD><TD >16</TD><TD >71</TD></tr>\n" );
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document.write( "That way each value is now a whole number.\r<BR>\n" );
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document.write( "Let's compute the row and column totals.<BR>\n" );
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document.write( "<tr><TD ></TD><TD >Smoker</TD><TD >Nonsmoker</TD><TD >Total</TD></tr><tr><TD >Lung Disease</TD><TD >10</TD><TD >3</TD><TD >13</TD></tr><tr><TD >No Lung Disease</TD><TD >16</TD><TD >71</TD><TD >87</TD></tr><tr><TD >Total</TD><TD >26</TD><TD >74</TD><TD >100</TD></tr>\n" );
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document.write( "Example: 10+3 = 13 at the end of row 1.\r<BR>\n" );
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document.write( "Part (A)\r<BR>\n" );
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document.write( "There are 26 smokers out of 100 men total.<BR>\n" );
document.write( "P(smoker) = 26/100 = 0.26\r<BR>\n" );
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document.write( "Or alternatively you can add the decimal values along column 1 to get: 0.1+0.16 = 0.26\r<BR>\n" );
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document.write( "Part (B)\r<BR>\n" );
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document.write( "87 men do not have lung disease out of 100 total.<BR>\n" );
document.write( "P(no lung disease) = 87/100 = 0.87\r<BR>\n" );
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document.write( "Or alternatively you can add the decimal values along row 2 to get: 0.16+0.71= 0.87\r<BR>\n" );
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document.write( "Part (C)\r<BR>\n" );
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document.write( "\"given that he is a smoker\" means we know 100% the randomly selected person smokes.<BR>\n" );
document.write( "We focus on the \"smoker\" column only.\r<BR>\n" );
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document.write( "Of the 26 total people here, 10 have lung disease.<BR>\n" );
document.write( "P(lung disease given smoker) = 10/26 = 5/13 = 0.384615 approximately<BR>\n" );
document.write( "It's roughly a 38.46% chance\r<BR>\n" );
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document.write( "Part (D)\r<BR>\n" );
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document.write( "This time we focus on the \"nonsmoker\" column because we're told \"given that he does not smoke\".\r<BR>\n" );
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document.write( "3 nonsmokers have lung disease out of 74 nonsmokers total.<BR>\n" );
document.write( "P(lung disease given nonsmoker) = 3/74 = 0.040541 approximately<BR>\n" );
document.write( "It's roughly a 4.05% chance<BR>\n" );
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