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Mathematics > Standard Multiple Choice

A number cube, with faces numbered through , is to be rolled twice. What is the probability that the number that comes up on the first roll will be less than the number that comes up on the second roll?

# Yep! That's right.

### Explanation

The outcome space for this experiment is the set of all ordered pairs where represents the first number that comes up, and represents the second one. Since  and can take all the values  through , there will be a total of possible outcomes. The outcomes can be represented in a table as shown:

Among all the pairs , are pairs for which . So remaining pairs will have . Notice that the number of pairs  for which is the same with the number of pairs

for which . Therefore the number of pairs

for which , is (half of ). Then the probability that is equal to .

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