document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026168>Question 1026168</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An urn contains 3 red balls and 7 green balls. A ball is drawn randomly and in its place are put 2 of the opposite color. Then another ball is drawn randomly. Find the conditional probability that the first ball was green given that the second ball is red. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641466 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=641466\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have to find P(G1|R2) = P(G1 &#8745; R2)/P(R2).\r<BR>\n" );
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document.write( "By the law of total probability,<BR>\n" );
document.write( "P(R2) = P(G1 &#8745; R2)+P(R1 &#8745; R2) = P(R2|G1)P(G1) + P(R2|R1)P(R1) \r<BR>\n" );
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document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F10%29%2A%285%2F11%29+%2B+%283%2F10%29%2A%282%2F11%29+=+35%2F110+%2B+6%2F110+=+41%2F110 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==>P(G1|R2) = P(G1 &#8745; R2)/P(R2) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835%2F110%29%2F%2841%2F110%29+=+35%2F41 ALIGN=MIDDLE  ALT=\"%2835%2F110%29%2F%2841%2F110%29+=+35%2F41\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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