document.write( "Question 1191169: A box contains 7 identical marbles, except for color, of which 4 are red and 3 are green. Two
\n" ); document.write( "marbles are selected at random (a) one by one with replacement; (b) one by one without
\n" ); document.write( "replacement; (c) two marbles together.
\n" ); document.write( "Compute the numbers of sample points in all these cases
\n" ); document.write( "

Algebra.Com's Answer #822951 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
A box contains 7 identical marbles, except for color, of which 4 are red and 3 are green.
\n" ); document.write( "Two marbles are selected at random (a) one by one with replacement; (b) one by one without
\n" ); document.write( "replacement; (c) two marbles together.
\n" ); document.write( "Compute the numbers of sample points in all these cases
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Part  (c)  is  IDENTICAL  to part  (b).   THEREFORE,  there is no sense to consider part  (c)  separately,\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "and I will not consider part  (c)  separately.   It is covered by part  (b),  in full.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                 Part  (a)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The sample space consists of 4 elements  RR, RG, GR, GG with the probabilities\r\n" );
document.write( "\r\n" );
document.write( "    P(RR) = \"%284%2F7%29%2A%284%2F7%29\" = \"16%2F49\";\r\n" );
document.write( "\r\n" );
document.write( "    P(RG) = \"%284%2F7%29%2A%283%2F7%29\" = \"12%2F49%29\";\r\n" );
document.write( "\r\n" );
document.write( "    P(GR) = \"%283%2F7%29%2A%284%2F7%29\" = \"12%2F49\";\r\n" );
document.write( "\r\n" );
document.write( "    P(GG) = \"%283%2F7%29%2A%283%2F7%29\" = \"9%2F49\"\r\n" );
document.write( "\r\n" );
document.write( "with the total sum  P((RR) + P(RG) + P(GR) + P(GG) = 1.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Part  (a)  is complete.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                 Part  (b)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "The sample space consists of 4 elements  RR, RG, GR, GG with the probabilities\r\n" );
document.write( "\r\n" );
document.write( "    P(RR) = \"%284%2F7%29%2A%283%2F6%29\" = \"2%2F7\";\r\n" );
document.write( "\r\n" );
document.write( "    P(RG) = \"%284%2F7%29%2A%283%2F6%29\" = \"2%2F7%29\";\r\n" );
document.write( "\r\n" );
document.write( "    P(GR) = \"%283%2F7%29%2A%284%2F6%29\" = \"2%2F7\";\r\n" );
document.write( "\r\n" );
document.write( "    P(GG) = \"%283%2F7%29%2A%282%2F6%29\" = \"1%2F7\"\r\n" );
document.write( "\r\n" );
document.write( "with the total sum  P((RR) + P(RG) + P(GR) + P(GG) = 1.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Part  (b)  is complete.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The problem is solved,  in full.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );