Two dice are thrown simultaneously. given that sum of the numbers is not more than 5, what is the probability that sum is more than 3?

A method to know the probability is to list down all of the possible combinations that would present an outcome of not more than 5. This is listed below:

1 + 4
4 + 1
2 + 3
3 + 2
1 + 1
2 + 2
1 + 2
2 + 1
1 + 3
3 + 1

There are 10 possible outcomes. But among these, the only ones that can have a sum more than 3 are:

1 + 4
4 + 1
2 + 3
3 + 2
2 + 2
1 + 3
3 + 1

There are only 7 possible outcomes that meet both requirements. Given that there are 7 outcomes within the total of 10, the probability would be 7/10, or 0.7.

The vertex of the quadratic function is (1.5, -.75)