document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019204>Question 1019204</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The personnel manager of a manufacturing company has cross-classified the 400 employees of his company according to their record of absenteeism last year, and whether or not they were smokers, as shown in the following table.<BR>\n" );
document.write( "Number of days absent	Smoker	Nonsmoker<BR>\n" );
document.write( "Less than 10	         34	260<BR>\n" );
document.write( "10 or more	         78	28\r<BR>\n" );
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document.write( "If one of these employees is selected at random.<BR>\n" );
document.write( "a.	What is the probability that the employee selected was a non-smoker?<BR>\n" );
document.write( "b.	What is the probability that the employee selected was absent for 10 or more days?<BR>\n" );
document.write( "c.	Are the events “non-smoker” and “absent less than 10 days” mutually exclusive?  Explain.<BR>\n" );
document.write( "d.	What is the probability that the employee selected was absent for less than 10 days given that the employee is a smoker?<BR>\n" );
document.write( "e.	What is the probability that the employee selected was absent for less than 10 days given that the employee does not smoke?<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 #635213 by </B><A HREF=/tutors/aboutme.mpl?userid=robertb><B>robertb(5830)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=robertb><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=robertb><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635213\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. (28+260)/400 = 18/25\r<BR>\n" );
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document.write( "b. (78+28)/400 = 53/200\r<BR>\n" );
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document.write( "c. The two events are mutually exclusive if P(\"non-smoker\" and \"absent less than 10 days\") = 0. Since from the data, P(\"non-smoker\" and \"absent less than 10 days\") = 260/400 = 13/20, the two events are NOT mutually exclusive.\r<BR>\n" );
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document.write( "d.  P(\"absent for less than 10 days\"|smoker) =  P(\"absent for less than 10 days\" AND smoker)/P(smoker) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2834%2F400%29%2F%287%2F25%29+=+17%2F56 ALIGN=MIDDLE  ALT=\"%2834%2F400%29%2F%287%2F25%29+=+17%2F56\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "e.  P(\"absent for less than 10 days\"|non-smoker) =  P(\"absent for less than 10 days\" AND non-smoker)/P(non-smoker) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28260%2F400%29%2F%2818%2F25%29+=+65%2F72 ALIGN=MIDDLE  ALT=\"%28260%2F400%29%2F%2818%2F25%29+=+65%2F72\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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