Given a die, what is the probability that the second roll of a die will be less than the first roll? If you are given a die and asked to roll it twice. What is the probability that the value of the second roll will be less than the value of the first roll?

If the:
first roll is a 6 odds are: 5/6
first roll is a 5 odds are: 4/6
first roll is a 4 odds are: 3/6
first roll is a 3 odds are: 2/6
first roll is a 2 odds are: 1/6
first roll is a 1 odds are: 0/6

Therefore the total odds are the average of all those roll possibilities so:
$$
    \frac{\frac{5}{6} + \frac{4}{6} + \frac{3}{6} + \frac{2}{6} + \frac{1}{6} + \frac{0}{6}}{6} = \frac{\frac{15}{6}}{6} = \frac{15}{36} = \frac{5}{12} = \frac{2.5}{6}
$$
