Here are two approaches:
a) Count up the possibilities. If the first die is 1, there are 5
greater numbers on the second: 1/6 * 5/6 = 5/36. If the first die
is 2, there are 4: 1/6 * 4/6 = 4/36. Etc. The result:
5/36 + 4/ 36 + 3/36 + 2/36 + 1/36 = 15/36 = 5/12.
b) You can assume that, as long as the dice don't show matching
numbers, there's an even chance that either the first or the second
is greater. So the probability that the first is less is 1/2 the
probability that the dice don't match.
There's a 1/6 chance that the dice do match. So the probability of
non-matching is 5/6, and the probability that the first is less
than the second is 5/12.
4. Two fair dice are rolled. Compute the probability that the number on the first is...
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