document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=836154>Question 836154</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a box contains 7 identical red balls, 4 identical white balls and 9 identical black balls. 3 balls are taken out from the box one after another without replacement. what the probability that \r<BR>\n" );
document.write( "\n" );
document.write( "i)2 of them are red and one is black<BR>\n" );
document.write( "ii)all three balls have different colour<BR>\n" );
document.write( "iii) at least one ball is white<BR>\n" );
document.write( "iv)all three have same colour </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #503992 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=503992\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a box contains 7 identical red balls, 4 identical white balls and 9 identical black balls. 3 balls are taken out from the box one after another without replacement. what the probability that <BR>\n" );
document.write( "i)2 of them are red and one is black<BR>\n" );
document.write( "# of ways to succeed:: 7C2*9 = 21*9 = 189<BR>\n" );
document.write( "# of random triples: 20C3 = 1140<BR>\n" );
document.write( "P(2red AND 1black) = 189/1140<BR>\n" );
document.write( "---------------------------------------------<BR>\n" );
document.write( "ii)all three balls have different colour<BR>\n" );
document.write( "# of ways to succeed:: 7*4*9 = 252<BR>\n" );
document.write( "# of random triples: 1140<BR>\n" );
document.write( "P(diff colors) = 252/1140<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "iii) at least one ball is white::<BR>\n" );
document.write( "P(at least one white) 1 - P(no white)<BR>\n" );
document.write( "P(no white) = (11/16)^3 = 0.325<BR>\n" );
document.write( "P(at least one white = 1-0.325 = 0.675<BR>\n" );
document.write( "======================================<BR>\n" );
document.write( "iv)all three have same colour<BR>\n" );
document.write( "# of ways to succeed: 9C3+7C3+4C3 = 123<BR>\n" );
document.write( "P(all same color) = 123/1140<BR>\n" );
document.write( "=====================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "=========================<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );