document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=945409>Question 945409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bottle 1 consists of 4 red balls and 6 blue balls.  Bottle 2 consists of some unknown number of red balls and 12 blue balls.  One ball is drawn from each bottle. The probability that both balls are red or both balls are blue is 0.56.  Find the number of red balls in bottle 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #576543 by </B><A HREF=/tutors/aboutme.mpl?userid=mathmate><B>mathmate(429)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mathmate><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=mathmate><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=576543\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">   <BR>\n" );
document.write( "Given:<BR>\n" );
document.write( "Two bottles containing red and blue balls.<BR>\n" );
document.write( "Bottle 1: 4R+6B<BR>\n" );
document.write( "Bottle 2: xR+12B<BR>\n" );
document.write( "One ball is drawn from each bottle.<BR>\n" );
document.write( "P(RR&cup;BB)=0.56 (i.e. probability of drawing both red or both blue)<BR>\n" );
document.write( "Find x (number of red balls in bottle 2).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "Solution:<BR>\n" );
document.write( "Let <BR>\n" );
document.write( "R=event of drawing a red ball<BR>\n" );
document.write( "B=event of drawing a blue ball<BR>\n" );
document.write( "Since events of drawing from different bottles are independent, we can multiply the individual probabilities, i.e.<BR>\n" );
document.write( "P(RR)=P(R) from bottle 1  *  P(R) from bottle 2, and similarly for P(BB)<BR>\n" );
document.write( "  <BR>\n" );
document.write( "P(RR)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F%284%2B6%29%29%2A%28x%2F%28x%2B12%29%29=0.4x%2F%28x%2B12%29 ALIGN=MIDDLE  ALT=\"%284%2F%284%2B6%29%29%2A%28x%2F%28x%2B12%29%29=0.4x%2F%28x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "P(BB)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2F%284%2B6%29%29%2A%2812%2F%28x%2B12%29%29=7.2%2F%28x%2B12%29 ALIGN=MIDDLE  ALT=\"%286%2F%284%2B6%29%29%2A%2812%2F%28x%2B12%29%29=7.2%2F%28x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since the events RR and BB are mutually exclusive, probability of the union is the sum of the individual probabilities.<BR>\n" );
document.write( "P(RR&cup;BB)=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4x%2F%28x%2B12%29%2B7.2%2F%28x%2B12%29 ALIGN=MIDDLE  ALT=\"0.4x%2F%28x%2B12%29%2B7.2%2F%28x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is given to be 0.56<BR>\n" );
document.write( "So we have an equation in x from which we can solve for x:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4x%2F%28x%2B12%29%2B7.2%2F%28x%2B12%29+=+0.56 ALIGN=MIDDLE  ALT=\"0.4x%2F%28x%2B12%29%2B7.2%2F%28x%2B12%29+=+0.56\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.4x%2B7.2=0.56%28x%2B12%29 ALIGN=MIDDLE  ALT=\"0.4x%2B7.2=0.56%28x%2B12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.2-6.72=0.16x ALIGN=MIDDLE  ALT=\"7.2-6.72=0.16x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0.48%2F0.16=3 ALIGN=MIDDLE  ALT=\"x=0.48%2F0.16=3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "Answer:<BR>\n" );
document.write( "There are 3 red balls in the second bottle. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );