Three dice are tossed. Find the probability of rolling a sum greater than 5.
\n" );
document.write( "\r\n" );
document.write( "We find the probability of the complement and subtract from 1.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "There are only 10 possible rolls with sums that are NOT greater than 5.\r\n" );
document.write( "They are these:\r\n" );
document.write( "\r\n" );
document.write( " 1. (1,1,1)\r\n" );
document.write( " 2. (1,1,2)\r\n" );
document.write( " 3. (1,1,3)\r\n" );
document.write( " 4. (1,2,1)\r\n" );
document.write( " 5. (1,2,2)\r\n" );
document.write( " 6. (1,3,1)\r\n" );
document.write( " 7. (2,1,1)\r\n" );
document.write( " 8. (2,1,2)\r\n" );
document.write( " 9. (2,2,1)\r\n" );
document.write( "10. (3,1,1)\r\n" );
document.write( "\r\n" );
document.write( "So the numerator (before reducing) of the probability of the complement event\r\n" );
document.write( "is 10.\r\n" );
document.write( "\r\n" );
document.write( "We calculate the number of ways the dice can land.\r\n" );
document.write( "\r\n" );
document.write( "The first one can land any of 6 ways.\r\n" );
document.write( "For every way the first one can land, the second one can land 6 ways.\r\n" );
document.write( "So the first two can land 6∙6 or 36 ways.\r\n" );
document.write( "For every way the first two can land, the third one can land 6 ways.\r\n" );
document.write( "So there are 6∙6∙6 = 36∙6 = 216 ways the three dice can land.\r\n" );
document.write( "\r\n" );
document.write( "So the denominator (before reducing) of the probability of the complement event\r\n" );
document.write( "is 216.\r\n" );
document.write( "\r\n" );
document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" );
document.write( "![\"\"](\"/images/stars/stars-13.gif\")
