document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168580>Question 1168580</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two marbles are drawn without replacement from a box with 3 white, 2 green, and 2 red and 1 blue marble: Find the probability: One marble is green and one marble is red  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793155 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=793155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the box has 3 white, 2 green, 2 red, 1 blue marble.<BR>\n" );
document.write( "if you draw 2 marbles from the box, you want to know the probability that one of those marbles is red and one of those marbles is green.\r<BR>\n" );
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document.write( "couple of ways to solve this.\r<BR>\n" );
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document.write( "one way is to use the combination formula.<BR>\n" );
document.write( "the number of ways you can get a set of 2 out of a set of 8 is c(8,2) = 28<BR>\n" );
document.write( "the number of ways you can get a set of 1 green out of a set of 2 greens is c(2,1) = 2.<BR>\n" );
document.write( "the number of ways you can get a set of 1 red out of a set of 2 reds is c(2,1) = 2.<BR>\n" );
document.write( "the probability of getting a red and a green out of a set of 8 is therefore (2*2)/28 = 4/28 = 1/7.\r<BR>\n" );
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document.write( "another way is to determine  that the probability of getting a green and a red out of a set of 8 that contains 2 greens and 2 reds is:<BR>\n" );
document.write( "p(first green and then red) = 2/8 * 2/7 = 4/56.<BR>\n" );
document.write( "p(first red and then green) = 2/8 * 2/7 = 4/56.<BR>\n" );
document.write( "total probability is p(first green and then red) + p(first red and then green) = 8/56.<BR>\n" );
document.write( "simplify to get 1/7.\r<BR>\n" );
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document.write( "both ways assume drawing without replacement.<BR>\n" );
document.write( "both ways get the same answer.<BR>\n" );
document.write( "the answer appears to be 1/7.\r<BR>\n" );
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document.write( "the combination formula says c(n,x) = n! / (x! * (n-x)!)<BR>\n" );
document.write( "then n = 8 and x = 2, that formula becomes 8! / (2! * 6!)<BR>\n" );
document.write( "8! can be shown as (8 * 7 * 6!)<BR>\n" );
document.write( "the formula becomes (8 * 7 * 6!) / (2! * 6!)<BR>\n" );
document.write( "6! cancels out, so the formula becomes (8 * 7) / (2 * 1)<BR>\n" );
document.write( "solve to get c(8,2) = 56/2 = 28.<BR>\n" );
document.write( "that was the denominator in the first way to solve the problem.\r<BR>\n" );
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