document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158482>Question 1158482</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Refer to the contingency table shown below.<BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "Smoking by Race for Males Aged 18-24<BR>\n" );
document.write( " 	Smoker<BR>\n" );
document.write( "(S)	Nonsmoker<BR>\n" );
document.write( "(N)	Row Total<BR>\n" );
document.write( "White(W)	 	290	 	 	560	 	 	850	 <BR>\n" );
document.write( "Black(B)	 	30	 	 	120	 	 	150	 <BR>\n" );
document.write( "Column Total	 	320	 	 	680	 	 	1,000	 <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Click here for the Excel Data File<BR>\n" );
document.write( " <BR>\n" );
document.write( "(a) Calculate the probabilities given below (Round your answers to 4 decimal places.):<BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " 	 	 <BR>\n" );
document.write( "i.P(S)	0.3200 0.3200 Correct	 <BR>\n" );
document.write( "ii.P(W)	0.8500 0.8500 Correct	 <BR>\n" );
document.write( "iii.P(S | W)	0.2720 0.2720 Incorrect	 <BR>\n" );
document.write( "iv.P(S | B)	0.0300 0.0300 Incorrect	 <BR>\n" );
document.write( "v. P(S and W)	0.9062 0.9062 Incorrect	 <BR>\n" );
document.write( "vi.P(N and B)	0.1765 0.1765 Incorrect	 <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781438 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=781438\">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<BR>\n" );
document.write( "<TABLE  border = \"1\" cellpadding = \"5\">\n" );
document.write( "\r\n" );
document.write( "<tr><TD ></TD><TD >Smoker (S)</TD><TD >Nonsmoker (N)</TD><TD >Row Total</TD></tr>\r\n" );
document.write( "<tr><TD >White (W)</TD><TD >290</TD><TD >560</TD><TD >850</TD></tr>\r\n" );
document.write( "<tr><TD >Black (B)</TD><TD >30</TD><TD >120</TD><TD >150</TD></tr>\r\n" );
document.write( "<tr><TD >Column Total</TD><TD >320</TD><TD >680</TD><TD >1000</TD></tr>\r\n" );
document.write( "\n" );
document.write( "</TABLE>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "S = smoker<BR>\n" );
document.write( "N = nonsmoker<BR>\n" );
document.write( "W = white male aged 18-24<BR>\n" );
document.write( "B = black male aged 18-24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part i.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(S) = probability of selecting a smoker<BR>\n" );
document.write( "P(S) = (number of smokers)/(number total)<BR>\n" );
document.write( "P(S) = 320/1000<BR>\n" );
document.write( "P(S) = 0.3200\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.3200</font>\r<BR>\n" );
document.write( "\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part ii.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(W) = probability of selecting a white male<BR>\n" );
document.write( "P(W) = (number of white males)/(number total)<BR>\n" );
document.write( "P(W) = 850/1000<BR>\n" );
document.write( "P(W) = 0.8500\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.8500</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Nice work on getting parts i and ii correct.<BR>\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part iii.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(S|W) = probability of selecting a smoker (S) given they are white male (W)<BR>\n" );
document.write( "P(S|W) = (number of white male smokers)/(number of white males)<BR>\n" );
document.write( "P(S|W) = 290/850<BR>\n" );
document.write( "P(S|W) = 0.341176471 which is approximate<BR>\n" );
document.write( "P(S|W) = 0.3412 rounded to four decimal places\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "notice how we only focus on the white male row since we are given the person is a white male. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.3412</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part iv.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This time we focus on the black male row. Ignore everything else.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "There are 30 who smoke out of 150 total<BR>\n" );
document.write( "P(S|B) = probability of selecting a smoker (S) given they are a black male (B)<BR>\n" );
document.write( "P(S|B) = 30/150<BR>\n" );
document.write( "P(S|B) = 0.2000\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.2000</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part v.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This time we consider all males surveyed since we don't have a conditional probability.<BR>\n" );
document.write( "P(S and W) = probability of selecting a smoker and a white male<BR>\n" );
document.write( "P(S and W) = (number of smokers who are white)/(number of people total)<BR>\n" );
document.write( "P(S and W) = 290/1000<BR>\n" );
document.write( "P(S and W) = 0.2900\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.2900</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "==================================================<BR>\n" );
document.write( "Part vi.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "P(N and B) = probability of selecting a nonsmoker and a black male<BR>\n" );
document.write( "P(N and B) = (number of nonsmokers who are black)/(number of people total)<BR>\n" );
document.write( "P(N and B) = 30/1000<BR>\n" );
document.write( "P(N and B) = 0.0300\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer: <font color=red size=4>0.0300</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );