document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=878855>Question 878855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A bag contains a red marble, a blue marble and a yellow marble.  A marble is selected at random 3 times with replacement.  How many events will form a full group of events?  Also, list all of these events in which the first draw results in a red marble being selected. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #530336 by </B><A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><B>AnlytcPhil(1810)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=AnlytcPhil><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=AnlytcPhil><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=530336\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "There are 3 ways to draw the first marble.\r\n" );
document.write( "For each of these 3 ways to draw the first marble,\r\n" );
document.write( "there are 3 ways to draw the second marble.\r\n" );
document.write( "That's 3×3 or 9 ways to draw the first two marbles.\r\n" );
document.write( "For each of these 9 ways to draw the first two marbles,\r\n" );
document.write( "there are 3 ways to draw the third marble.\r\n" );
document.write( "That's 9×3 or 27 ways to draw all three marbles.\r\n" );
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document.write( "Here they are listed two ways:\r\n" );
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document.write( "You can list them with a tree diagram like this: \r\n" );
document.write( " \r\n" );
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document.write( "                                     R = RRR\r\n" );
document.write( "                                    /\r\n" );
document.write( "                                   R-B = RRB\r\n" );
document.write( "                                  / \\r\n" );
document.write( "                                 /   Y = RRY\r\n" );
document.write( "                                /\r\n" );
document.write( "                               /     R = RBR\r\n" );
document.write( "                              /     /\r\n" );
document.write( "                             R-----B-B = RBB\r\n" );
document.write( "                            / \     \\r\n" );
document.write( "                           /   \     Y = RBY\r\n" );
document.write( "                          /     \\r\n" );
document.write( "                         /       \   R = RYR\r\n" );
document.write( "                        /         \ /\r\n" );
document.write( "                       /           Y-B = RYB\r\n" );
document.write( "                      /             \\r\n" );
document.write( "                     /               Y = RYY\r\n" );
document.write( "                    /\r\n" );
document.write( "                   /                 R = BRR\r\n" );
document.write( "                  /                 /\r\n" );
document.write( "                 /                 R-B = BRB\r\n" );
document.write( "                /                 / \\r\n" );
document.write( "               /                 /   Y = BRY\r\n" );
document.write( "              /                 /\r\n" );
document.write( "             /                 /     R = BBR\r\n" );
document.write( "            /                 /     /\r\n" );
document.write( "     START /-----------------B-----B-B = BBB\r\n" );
document.write( "            \                 \     \\r\n" );
document.write( "             \                 \     Y = BBY\r\n" );
document.write( "              \                 \\r\n" );
document.write( "               \                 \   R = BYR\r\n" );
document.write( "                \                 \ /\r\n" );
document.write( "                 \                 Y-B = BYB\r\n" );
document.write( "                  \                 \\r\n" );
document.write( "                   \                 Y = BYY\r\n" );
document.write( "                    \\r\n" );
document.write( "                     \               R = YRR\r\n" );
document.write( "                      \             /\r\n" );
document.write( "                       \           R-B = YRB\r\n" );
document.write( "                        \         / \\r\n" );
document.write( "                         \       /   Y = YRY\r\n" );
document.write( "                          \     /\r\n" );
document.write( "                           \   /     R = YBR\r\n" );
document.write( "                            \ /     /\r\n" );
document.write( "                             Y-----B-B = YBB\r\n" );
document.write( "                              \     \\r\n" );
document.write( "                               \     Y = YBY\r\n" );
document.write( "                                \\r\n" );
document.write( "                                 \   R = YYR\r\n" );
document.write( "                                  \ /\r\n" );
document.write( "                                   Y-B = YYB\r\n" );
document.write( "                                    \\r\n" );
document.write( "                                     Y = YYY\r\n" );
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document.write( "Or you can just list them all like this:\r\n" );
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document.write( " 1. Red first, Red second, Red third\r\n" );
document.write( " 2. Red first, Red second, Blue third\r\n" );
document.write( " 3. Red first, Red second, Yellow third\r\n" );
document.write( " 4. Red first, Blue second, Red third\r\n" );
document.write( " 5. Red first, Blue second, Blue third\r\n" );
document.write( " 6. Red first, Blue second, Yellow third\r\n" );
document.write( " 7. Red first, Yellow second, Red third\r\n" );
document.write( " 8. Red first, Yellow second, Blue third\r\n" );
document.write( " 9. Red first, Yellow second, Yellow third\r\n" );
document.write( "10. Blue first, Red second, Red third\r\n" );
document.write( "11. Blue first, Red second, Blue third\r\n" );
document.write( "12. Blue first, Red second, Yellow third\r\n" );
document.write( "13. Blue first, Blue second, Red third\r\n" );
document.write( "14. Blue first, Blue second, Blue third\r\n" );
document.write( "15. Blue first, Blue second, Yellow third\r\n" );
document.write( "16. Blue first, Yellow second, Red third\r\n" );
document.write( "17. Blue first, Yellow second, Blue third\r\n" );
document.write( "18. Blue first, Yellow second, Yellow third\r\n" );
document.write( "19. Yellow first, Red second, Red third\r\n" );
document.write( "20. Yellow first, Red second, Blue third\r\n" );
document.write( "21. Yellow first, Red second, Yellow third\r\n" );
document.write( "22. Yellow first, Blue second, Red third\r\n" );
document.write( "23. Yellow first, Blue second, Blue third\r\n" );
document.write( "24. Yellow first, Blue second, Yellow third\r\n" );
document.write( "25. Yellow first, Yellow second, Red third\r\n" );
document.write( "26. Yellow first, Yellow second, Blue third\r\n" );
document.write( "27. Yellow first, Yellow second, Yellow third\r\n" );
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document.write( "Edwin</PRE> </SPAN>\n" );
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