Question

You roll 1 red and 1 white die. What is the probability that the number on the red die is larger than the number on the white die?

Answer 1

There are various ways to answer this. Here is one:

There is clearly a 1 out of 6 chance that the two rolls will be the same, hence a 5 out of 6 chance that they will be different. Further, the chance that the first roll is greater than the second must be equal to the chance that the second roll is greater than the first (e.g. switch the two dice!), so both chances must be 2.5 out of 6 or 5 out of 12.

In the end, the chance is: 5/12