document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183702>Question 1183702</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you work for a small company with delivery vans. The business has three drivers who deliver packages to private individuals.\r<BR>\n" );
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document.write( "Driver 1 takes 30% of the runs but delivers to the wrong address in 5% of the runs\r<BR>\n" );
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document.write( "Driver 2 takes 20% of the journeys but delivers to the wrong address in 2% of the journeys\r<BR>\n" );
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document.write( "Driver 3 takes 50% of the runs but delivers to the wrong address in 10% of the runs\r<BR>\n" );
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document.write( "1. What proportion of deliveries go to the right address?\r<BR>\n" );
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document.write( "2. What is the probability that the latest package that arrived at the correct address was delivered by Driver 3?\r<BR>\n" );
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document.write( "3. Assume that you have now received a complaint from a customer who has not received their package. What is the probability that that delivery would have been delivered by Driver 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814134 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=814134\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. P(correct address) = P(correct address AND driver 1) + P(correct address AND driver 2) + P(correct address AND driver 3) = 0.285 + 0.196 + 0.45 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.931%29 ALIGN=MIDDLE  ALT=\"highlight%280.931%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "***<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28Note%29 ALIGN=MIDDLE  ALT=\"highlight%28Note%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >:  Compare the final answer with that of tutor ikleyn, whose final answer is 0.391, which is a mis-arrangment of digits of the correct final answer.  <BR>\n" );
document.write( "(Rather funny)\r<BR>\n" );
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document.write( "2.  P(driver 3| correct address) = P(correct address AND driver 3)/P(correct address) = 0.45/0.931 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.48335%29 ALIGN=MIDDLE  ALT=\"highlight%280.48335%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (5 d.p.)\r<BR>\n" );
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document.write( "3.  P(driver 1| wrong address) = P(wrong address AND driver 1)/P(wrong address) = 0.015/0.069 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.21739%29 ALIGN=MIDDLE  ALT=\"highlight%280.21739%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  (5 d.p.)<BR>\n" );
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