document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=430559>Question 430559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are two sets of marbles.  Both have 1,000 in them.  Bag 1 has 700 blue and 300 red.  Bag 2 has 300 blue and 700 red.  Picking a bag at random you draw out 10 marbles with replacement.  If 7 are red and 3 are blue, what is the exact probability of you picking Bag 1? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #299148 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=299148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The assumptions that \r<BR>\n" );
document.write( "\n" );
document.write( "P(7R3B|bag1) = C(10,3)[(.7)^7(.3)^3] \r<BR>\n" );
document.write( "\n" );
document.write( "P(7R3B|bag2) = C(10,3)[(.3)^7(.7)^3] <BR>\n" );
document.write( " <BR>\n" );
document.write( "are wrong.\r<BR>\n" );
document.write( "\n" );
document.write( "The experiment of drawing balls from each bag doesn't follow a binomial distribution, but a hypergeometric distribution.\r<BR>\n" );
document.write( "\n" );
document.write( "They should be <BR>\n" );
document.write( "P(7R3B|bag1) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28300C7%29%2A%28700C3%29%29%2F1000C10 ALIGN=MIDDLE  ALT=\"%28%28300C7%29%2A%28700C3%29%29%2F1000C10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "P(7R3B|bag2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28700C7%29%2A%28300C3%29%29%2F1000C10 ALIGN=MIDDLE  ALT=\"%28%28700C7%29%2A%28300C3%29%29%2F1000C10\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The use of Bayes' rule is correct.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );