document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174649>Question 1174649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A teacher has two boxes of pens. Box 1 contains 7 blue pens and 3 black<BR>\n" );
document.write( "pens, box 2 contains 2 blue pens and 8 black pens. The probability of<BR>\n" );
document.write( "selecting a pen from box 1 is 2<BR>\n" );
document.write( "3<BR>\n" );
document.write( "and the probability of selecting a pen<BR>\n" );
document.write( "from box 2 is 1<BR>\n" );
document.write( "3<BR>\n" );
document.write( ". If a pen is selected at random what is the probability<BR>\n" );
document.write( "that it is from box 1 given that it is black? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #800107 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=800107\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> P (box 1|black)=P(Black|box 1)*Box 1/P(black)<BR>\n" );
document.write( "=0.3*(2/3)/(14/30), the expected probability of a black pen's being chosen with the above probabilities.<BR>\n" );
document.write( "=2/10/14/30 or 2*3/14<BR>\n" );
document.write( "=0.429.\r<BR>\n" );
document.write( "\n" );
document.write( "another way<BR>\n" );
document.write( "-<BR>\n" );
document.write( "=====BLU- BLK-TOT<BR>\n" );
document.write( "Box 1--7----3---10<BR>\n" );
document.write( "Box 1--7----3---10<BR>\n" );
document.write( "Box 2-2----8---10]<BR>\n" );
document.write( "twice as many box 1 because 2/3 probability<BR>\n" );
document.write( "this leads to 16 blue an 14 black for a single choice which is where the 14/30 probability for a black comes from.<BR>\n" );
document.write( "Then given that a black pen is chosen (6/14), six came from box 1, so the probability is 0.429, equalling the one above. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );