document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=700038>Question 700038</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are three urns:first urn contains 1 white,2red,3green balls,second urn contains 2 white,1red,1green balls and third urn contains 4 white,5red,3green balls.<BR>\n" );
document.write( "Two balls are drawn from an urn chosen at random.These are found to be one white and one green.Probability that balls are drawn from third urn is:<BR>\n" );
document.write( "(A)15/59, (B)14/59, (C)13/59, (D)12/59\r<BR>\n" );
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document.write( "Please explain the procedure also!In book only the correct answer is given 15/59....but i dont get how to slove it,so plz explain the procedure,plz. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #431811 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431811\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> DISCLAIMER:<BR>\n" );
document.write( "I do not memorize procedures, and I do not follow procedures unless someone makes me.<BR>\n" );
document.write( "What follows is my just my understanding of the problem.<BR>\n" );
document.write( "Your teacher may have a procedure to reach the solution more efficiently.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If an urn chosen at random, the third urn will be chosen <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the times.<BR>\n" );
document.write( "(In fact, each of the three urns will be chosen <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F3 ALIGN=MIDDLE  ALT=\"1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the times).<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the first urn is chosen (with 6 balls, including 1 white and 3 green),<BR>\n" );
document.write( "the probability of drawing the white ball first is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F6 ALIGN=MIDDLE  ALT=\"1%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "After that, the probability of drawing one of the 3 green balls from the 5 balls left in the urn is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F5 ALIGN=MIDDLE  ALT=\"3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, the probability of drawing a white ball followed by a green ball from the first urn is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%283%2F5%29=1%2F10 ALIGN=MIDDLE  ALT=\"%281%2F6%29%283%2F5%29=1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Similarly, the probability of drawing a green ball followed by a white ball from the first urn is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2F6%29%281%2F5%29=1%2F10 ALIGN=MIDDLE  ALT=\"%283%2F6%29%281%2F5%29=1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "The probability of drawing a white ball and a green ball (in any order) from the first urn is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F10%2B1%2F10=1%2F5 ALIGN=MIDDLE  ALT=\"1%2F10%2B1%2F10=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " <BR>\n" );
document.write( "If the second urn is chosen (with 4 balls, including 2 white and 1 green),<BR>\n" );
document.write( "the probability of drawing a white ball and a green ball (in any order) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F4%29%281%2F3%29%2B%281%2F4%29%282%2F3%29=1%2F6%2B1%2F6=2%2F6=1%2F3 ALIGN=MIDDLE  ALT=\"%282%2F4%29%281%2F3%29%2B%281%2F4%29%282%2F3%29=1%2F6%2B1%2F6=2%2F6=1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If the third urn is chosen (with 12 balls, including 4 white and 3 green),<BR>\n" );
document.write( "the probability of drawing a white ball and a green ball (in any order) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F12%29%283%2F11%29%2B%283%2F12%29%284%2F11%29=1%2F11%2B1%2F11=2%2F11 ALIGN=MIDDLE  ALT=\"%284%2F12%29%283%2F11%29%2B%283%2F12%29%284%2F11%29=1%2F11%2B1%2F11=2%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "If the drawing of two balls was done <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2A%283%2A5%2A11%29=3%2A165 ALIGN=MIDDLE  ALT=\"3%2A%283%2A5%2A11%29=3%2A165\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "you would expect the first urn to be chosen 165 times,<BR>\n" );
document.write( "drawing one a white ball and a green ball (in any order) from the first urn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%281%2F5%29=3%2A5%2A11%282%2F5%29=3%2A11=highlight%2833%29 ALIGN=MIDDLE  ALT=\"165%281%2F5%29=3%2A5%2A11%282%2F5%29=3%2A11=highlight%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.<BR>\n" );
document.write( "The second urn would be also chosen 165 times,<BR>\n" );
document.write( "drawing one a white ball and a green ball (in any order) from the second urn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%281%2F3%29=3%2A5%2A11%281%2F3%29=5%2A11=highlight%2855%29 ALIGN=MIDDLE  ALT=\"165%281%2F3%29=3%2A5%2A11%281%2F3%29=5%2A11=highlight%2855%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.<BR>\n" );
document.write( "The third urn would be also chosen 165 times,<BR>\n" );
document.write( "drawing one a white ball and a green ball (in any order) from the third urn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=165%282%2F11%29=3%2A5%2A11%282%2F11%29=3%2A5%2A2=highlight%2830%29 ALIGN=MIDDLE  ALT=\"165%282%2F11%29=3%2A5%2A11%282%2F11%29=3%2A5%2A2=highlight%2830%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.<BR>\n" );
document.write( " <BR>\n" );
document.write( "In all, a white ball and a green ball (in any order) would be drawn (from an urn chosen at random)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=33%2B55%2B30=118 ALIGN=MIDDLE  ALT=\"33%2B55%2B30=118\"   DISABLED_style= \"max-width:90%; height:auto;\" > times.<BR>\n" );
document.write( "Of those 118 times, 30 times it would be from the third urn,<BR>\n" );
document.write( "so if a white ball and a green ball (in any order) had been drawn<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30%2F118=highlight%2815%2F59%29 ALIGN=MIDDLE  ALT=\"30%2F118=highlight%2815%2F59%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the times it would have been using the third urn.<BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );