document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=758269>Question 758269</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a box contain a four red, three black, and five white marble. two marbles are randomly drawn from this box and the color of these marbles is observed.\r<BR>\n" );
document.write( "\n" );
document.write( "1) write all the possible observations.<BR>\n" );
document.write( "2)calculate the probability of selecting two marbles of same color.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #461359 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=461359\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> see the following picture and the comments below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2013/jun151.png\" alt = \"$$$$$\"/><BR>\n" );
document.write( "you have 66 possible combinations of drawing 2 balls at a time taken from 12 balls.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is calculated by the combination formula of 12C2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "12C2 = (12*11) / (2*1) = 6*11 = 66\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of ways you can draw 2 red balls out of 4 = 4C2<BR>\n" );
document.write( "the number of ways you can draw 2 black balls out of 3 = 3C2<BR>\n" );
document.write( "the number of ways you can draw 2 white balls out of 5 = 5C2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "4C2 equals (4*3) / (2*1) = 6<BR>\n" );
document.write( "3C2 equals (3*2) / (2*1) = 3<BR>\n" );
document.write( "5C2 equals (5*4) / (2*1 = 10\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total ways you can get balls of the same color (either all red or all black or all white) equals 6 + 3 + 10 which equals 19.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the probability of getting all balls of the same color is therefore equal to 19 / 66.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );