document.write( "Question 1106734: We roll a fair die twice describe a sample space and a probability distribution P to model the experiment. Let A be the event that the second roll is larger than the first. Find P(A)?
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Algebra.Com's Answer #721726 by rothauserc(4718) $\"\"$ $\"About$

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There are 36 events in the sample space, namely
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\n" ); document.write( "(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
\n" ); document.write( "(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
\n" ); document.write( "(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
\n" ); document.write( "(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
\n" ); document.write( "(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
\n" ); document.write( "(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)
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\n" ); document.write( "this is a discrete probability distribution with the probability of each event = 1/36
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\n" ); document.write( "To find P(A) where second role > first role, we count the events where this is true for each row
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\n" ); document.write( "we inspect each row, 5 + 4 + 3 + 2 + 1 + 0 = 15
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\n" ); document.write( "P(A) = 15/36 = 5/12
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