document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=297867>Question 297867</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains 3 nickels, 4 dimes, and 5 quarters.  If two coins are selected at random without replacing the first one selected, what is the probability that the two coins match? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #214454 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=214454\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3 nickels<BR>\n" );
document.write( "4 dimes<BR>\n" );
document.write( "5 quarters<BR>\n" );
document.write( "12 total coins<BR>\n" );
document.write( "P(N)=3/12<BR>\n" );
document.write( "P(D)=4/12<BR>\n" );
document.write( "P(Q)=5/12<BR>\n" );
document.write( "Once one coin is chosen then the total number of coins drops to 11 and the probability of each coin is adjusted.<BR>\n" );
document.write( "P(N if nickel is chosen first)=2/11<BR>\n" );
document.write( "P(D if dime is chosen first)=3/11<BR>\n" );
document.write( "P(Q if quarter is chosen first)=4/11<BR>\n" );
document.write( "Since each event is independent, multiply the probabilities.<BR>\n" );
document.write( "P(nickel then nickel)=(3/12)(2/11)=1/22<BR>\n" );
document.write( "P(dime then dime)=(4/12)(3/11)=1/11<BR>\n" );
document.write( "P(quarter then quarter)=(5/12)(4/11)=5/33 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );