document.write( "Question 1137021: A fair pair of dice is rolled and the sum of the points is noted. What is the probability that one of the dice results in a point of 6​, given that the sum of the points is 8​? \n" ); document.write( "
Algebra.Com's Answer #754849 by greenestamps(13200)\"\" \"About 
You can put this solution on YOUR website!


\n" ); document.write( "The sample space for the problem is all the outcomes where the sum of the two dice is 8; the \"good\" outcomes are the ones that have a 6 on one of the two dice.

\n" ); document.write( "6+2
\n" ); document.write( "5+3
\n" ); document.write( "4+4
\n" ); document.write( "3+5
\n" ); document.write( "2+6

\n" ); document.write( "There are 5 ways to get a sum of 8; 2 of those ways have 6 on one of the two dice.

\n" ); document.write( "The probability that one of the dice shows 6, given that the sum of the two dice is 8, is 2/5.

\n" ); document.write( "Using the formal mathematical definition of conditional probability....
\r\n" );
document.write( "P(one of the dice is 6 | the sum of the two dice is 8)
\r\n" );
document.write( "= P((one of the dice is 6) AND (the sum of the dice is 8))    2/36     2\r\n" );
document.write( "  -------------------------------------------------------- = ------ = ---\r\n" );
document.write( "               P(sum of the dice is 8)                        5/36     5
\n" ); document.write( "
\n" );