document.write( "Question 1195890: A bag contains 8 red marbles, 3 blue marbles and 5 green marbles. If three marbles are drawn out of the bag, what is the exact probability that all three marbles drawn will be green?\r
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #828486 by ikleyn(52786)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "A bag contains 8 red marbles, 3 blue marbles and 5 green marbles.
\n" ); document.write( "If three marbles are drawn out of the bag, what is the exact probability
\n" ); document.write( "that all three marbles drawn will be green?
\n" ); document.write( "~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "At the start, there are  8 + 3 + 5 = 16  marbles in the bag.\r\n" );
document.write( "\r\n" );
document.write( "Of them, 5 marbles are green.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability that the first drawn marble is green equals  \"5%2F16\".\r\n" );
document.write( "\r\n" );
document.write( "After that, we have 15 marbles in the bag with 4 green marbles.\r\n" );
document.write( "So, the probability that the first two drawn marbles are green equals  \"%285%2F16%29%2A%284%2F15%29\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Analyzing further in the same way, we find that the probability\r\n" );
document.write( "that the first three drawn marbles are green equals \r\n" );
document.write( "\r\n" );
document.write( "    \"%285%2F16%29%2A%284%2F15%29%2A%283%2F14%29\" = reduce the fractions = \"%281%2F4%29%2A%281%2F3%29%2A%283%2F14%29\" = \"%281%2F4%29%2A%281%2F1%29%2A%281%2F14%29\" = \"1%2F56\".   ANSWER\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Ignore the solution by  @MathLover1,  since it is totally wrong.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is a good/classic example on how this problem  SHOULD  NOT  be solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Avoid such errors in the future  ( ! )\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "////////////////////\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "                        After reading the post by Alan, I find it necessary to explain \r
\n" ); document.write( "\n" ); document.write( "                            on how to read the problem and what does it really mean.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "        When such problem goes without explicit pointing on  \" with or without replacement \",\r
\n" ); document.write( "\n" ); document.write( "        then by  DEFAULT  and by the context,  it  ALWAYS  means  \" without replacement \".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );