document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=471378>Question 471378</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the constitution of 2 urns: first urn has 3 black balls and 2 whites<BR>\n" );
document.write( "second urn has 4 black balls and 6 whites.<BR>\n" );
document.write( "-> a draw is made by selecting an urn by a process which assigns probability P to the selection of urn I and probability 1-P to the selection of urn II. the selection of a ball from either urn is by a process which assigns equal probability to all balls in the urn. what value of P makes the probability of obtaining a black ball the same as if a single draw were made from an urn with 7 balck balls and 8 white balls (all balls are equally probable of being drawn).\r<BR>\n" );
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document.write( "thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #323500 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=323500\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equation is <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283p%29%2F5+%2B+%284%281-p%29%29%2F10+=+7%2F15 ALIGN=MIDDLE  ALT=\"%283p%29%2F5+%2B+%284%281-p%29%29%2F10+=+7%2F15\"   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=%283p%29%2F5+%2B+%282%281-p%29%29%2F5+=+7%2F15 ALIGN=MIDDLE  ALT=\"%283p%29%2F5+%2B+%282%281-p%29%29%2F5+=+7%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "==> 3p + 2(1-p) = 7/3, after multiplication by 5.\r<BR>\n" );
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document.write( "==> 3p + 2 - 2p = 7/3\r<BR>\n" );
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document.write( "==> p = 7/3-2\r<BR>\n" );
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document.write( "==> p = 1/3. </SPAN>\n" );
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