document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=394011>Question 394011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag has 3 red and k white marbles, where k is an (unknown) positive integer. Two of the marbles are chosen at random from the bag. If the probability that the two marbles are the same color is 1/2, find k. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #279570 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=279570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%3E=+2 ALIGN=MIDDLE  ALT=\"k%3E=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or else the event of getting 2 white marbles is excluded.\r<BR>\n" );
document.write( "\n" );
document.write( "The probability of getting 2 red marbles  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C2%2F%28k%2B3%29C2 ALIGN=MIDDLE  ALT=\"3C2%2F%28k%2B3%29C2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The probability of getting 2 white marbles  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kC2%2F%28k%2B3%29C2 ALIGN=MIDDLE  ALT=\"kC2%2F%28k%2B3%29C2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Hence <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3C2%2F%28k%2B3%29C2+%2B+kC2%2F%28k%2B3%29C2+=+1%2F2 ALIGN=MIDDLE  ALT=\"3C2%2F%28k%2B3%29C2+%2B+kC2%2F%28k%2B3%29C2+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2F%28%28k%2B3%29%28k%2B2%29%29+%2B+%28k%28k-1%29%29%2F%28%28k%2B3%29%28k%2B2%29%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"6%2F%28%28k%2B3%29%28k%2B2%29%29+%2B+%28k%28k-1%29%29%2F%28%28k%2B3%29%28k%2B2%29%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > after simplifying.<BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28k%5E2+-+k+%2B+6%29%2F%28k%5E2+%2B+5k+%2B+6%29+=+1%2F2 ALIGN=MIDDLE  ALT=\"%28k%5E2+-+k+%2B+6%29%2F%28k%5E2+%2B+5k+%2B+6%29+=+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<==> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2+-+7k+%2B+6+=+0 ALIGN=MIDDLE  ALT=\"k%5E2+-+7k+%2B+6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, after cross-multiplying and simplifying.<BR>\n" );
document.write( "<==> (k-1)(k - 6) = 0.<BR>\n" );
document.write( "==> k = 1, 6.<BR>\n" );
document.write( "Therefore k = 6, the number of white marbles. </SPAN>\n" );
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