document.write( "Question 1147640: A pair of dice are tossed twice.\r
\n" ); document.write( "\n" ); document.write( "Find the probability that the first roll is a total of at least 6 and the second roll is a total of at least 9. \n" ); document.write( "

Algebra.Com's Answer #768989 by ikleyn(52787) $\"\"$ $\"About$

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

\r\n" );
document.write( "\r\n" );
document.write( "When a pair of dice are tossed once, the sample space is the set of 36 pairs (a,b) of integer numbers \"a\" and \"b\"\r\n" );
document.write( "\r\n" );
document.write( "from 1 to 6 inclusively, with the probability    for each event (pair).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When a pair of dice are tossed twice, the sample space is the set of 36*36 pairs (a,b) and (x,y) of integer numbers \"a\", \"b\", x and y\r\n" );
document.write( "\r\n" );
document.write( "from 1 to 6 inclusively, with the probability    for each event (which is two pairs {(a,b),(x,y)} ).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability that the first roll is a total of at least 6 is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P( the total of the first tossing) >= 6) = P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P(6)  is       //   6 = 1+5 = 2+4 = 3+3 = 4+2 = 5+1\r\n" );
document.write( "\r\n" );
document.write( "    P(7)  is       //   7 = 1+6 = 2+5 = 3+4 = 4+3 = 5+2 = 6+1\r\n" );
document.write( "\r\n" );
document.write( "    P(8)  is       //   8 = 2+6 = 3+5 = 4+4 = 5+3 = 6+2\r\n" );
document.write( "\r\n" );
document.write( "    P(9)  is       //   9 = 3+6 = 4+5 = 5+4 = 6+3\r\n" );
document.write( "\r\n" );
document.write( "    P(10) is       //  10 = 4+6 = 5+5 = 6+4\r\n" );
document.write( "\r\n" );
document.write( "    P(11) is   \r\n" );
document.write( "\r\n" );
document.write( "    P(12) is   \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, P( the total of the first tossing) >= 6) =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The probability that the second roll is a total of at least 9 is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    P( the total of the second tossing) >= 9) = P(9) + P(10) + P(11) + P(12) =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "                \r\n" );
document.write( "\r\n" );
document.write( "The outcomes of the first and second rolls are INDEPENDENT, therefore, the final probability under the question is\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    . = .    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( "See the lesson\r
\n" ); document.write( "\n" ); document.write( " - Rolling a pair of fair dice \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );