document.write( "Question 1132894: Use the formula for the probability of the complement of an event.\r
\n" ); document.write( "\n" ); document.write( "Two dice are tossed. What is the probability of getting a sum of at least 3? (Enter your probability as a fraction.) \n" ); document.write( "

Algebra.Com's Answer #750058 by ikleyn(52921) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "The full space of events is the set of all pairs (m,n), where m and n are integers between 1 and 6 inclusively \r\n" );
document.write( "- possible outcomes from each dice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the full space of events has 6*6 = 36 elements, each with the probability of .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability of getting the sum at least of 3 is the sum of probabilities of getting 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12 (maximum).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The complement event is to get the sum of 2, which is possible for only one configuration (m,n) = (1,1) of the base space of events.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, the probability of getting this complement event is  .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Hence, the probability that the problem asking for is   = .     ANSWER\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "The problem is solved.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Thus using the complement space of events, we are free from the need to analyse all 35 events of the base space.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );