document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165286>Question 1165286</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The probability of being a smoker among a group of cases with lung cancer is<BR>\n" );
document.write( "0.75. Calculate the probability that in a group of 6 cases, you have at least 3<BR>\n" );
document.write( "smokers. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789754 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=789754\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "One less calculation to compute this as 1-Pr(2 or fewer smokers)<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Probability of nonsmoker is 1-0.75 = 0.25<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Probability of at least 3 smokers =  1 - (probability of 2 or fewer smokers)<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Probability of 0 smokers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.25%5E6+=+0.0002441+ ALIGN=MIDDLE  ALT=\"+0.25%5E6+=+0.0002441+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Probability of 1 smoker : <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.25%5E5+%2A+0.75%5E1+%2A+6C1+=+0.0043945+ ALIGN=MIDDLE  ALT=\"+0.25%5E5+%2A+0.75%5E1+%2A+6C1+=+0.0043945+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Probability of 2 smokers: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.25%5E4+%2A+0.75%5E2+%2A+6C2+=+0.0329590+ ALIGN=MIDDLE  ALT=\"+0.25%5E4+%2A+0.75%5E2+%2A+6C2+=+0.0329590+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<br><BR>\n" );
document.write( "Sum is 0.037598<BR>\n" );
document.write( "<br>\r<BR>\n" );
document.write( "\n" );
document.write( "Proability of at least 3 smokers = 1-0.037598 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+highlight%28+0.96240+%29+ ALIGN=MIDDLE  ALT=\"+highlight%28+0.96240+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "<br>\r<BR>\n" );
document.write( "\n" );
document.write( "You can try solving it in a direct method (pr(3)+pr(4)+pr(5)+pr(6) smokers) to prove to yourself that the answer comes out the same.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );