document.write( "Question 1098975: two 6-sided fair dice are thrown n times. let x denote the number of throws in which the result on the first die exceeds the results on the second die. what is the distribution of x? \n" ); document.write( "
Algebra.Com's Answer #713380 by Fombitz(32388)\"\" \"About 
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Let's look at the throws when the second die is a 1.
\n" ); document.write( "(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
\n" ); document.write( "This would lead to x=5 out of 6.
\n" ); document.write( "Similarly for the second die equal to 2.
\n" ); document.write( "(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
\n" ); document.write( "This gives x=4 out of 6.
\n" ); document.write( "All the way to the second die of 6.
\n" ); document.write( "(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
\n" ); document.write( "which has a x=0.
\n" ); document.write( "Summing them all,
\n" ); document.write( "\"x=5%2B4%2B3%2B2%2B1%2B0=15\"
\n" ); document.write( "So 15 out of 36 throws have the first dice exceeding the second.
\n" ); document.write( "Similarly 15 of 36 will have the second dice exceeding the first.
\n" ); document.write( "Finally 6 of 36 will have the first equal to the second.
\n" ); document.write( "\"15%2B15%2B6=36\"
\n" ); document.write( "\"36=36\"
\n" ); document.write( "There are no other possibilities.
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