document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=360608>Question 360608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An urn contains 14 balls; 6 of them are white, and the others are black.  Another urn contains 9 balls; 3 are white, and 6 are black.  A ball is drawn at random from the first urn and is placed in the second urn. Then, a ball is drawn at random from the second urn.  If this ball is white, find the probability that the ball drawn from the first urn was black.  \r<BR>\n" );
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document.write( "**Well, I know that I have to use the Law of Total Probability and the Bayes'Rule but I don't understand how.  \r<BR>\n" );
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document.write( "So much thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #257311 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=257311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let b1 = event that 1st ball drawn is black,<BR>\n" );
document.write( "w1 = event that 1st ball drawn is white,<BR>\n" );
document.write( "b2 = event that 2nd ball drawn is black,<BR>\n" );
document.write( "w2 = event that 2nd ball drawn is white.<BR>\n" );
document.write( "Then P(b1|w2) = P(b1 and w2)/P(w2)= P(b1 and w2)/[P(b1 and w2)+P(w1 and w2)]<BR>\n" );
document.write( "=P(w2|b1)*P(b1)/[P(w2|b1)*P(b1) + P(w2|w1)*P(w1)]<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F10%29%2A%284%2F7%29%2F%28%283%2F10%29%2A%284%2F7%29%2B%282%2F5%29%2A%283%2F7%29%29 ALIGN=MIDDLE  ALT=\"%283%2F10%29%2A%284%2F7%29%2F%28%283%2F10%29%2A%284%2F7%29%2B%282%2F5%29%2A%283%2F7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2F70%29%2F%2812%2F70%2B6%2F35%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%2812%2F70%29%2F%2812%2F70%2B6%2F35%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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