Mario has a number cube with sides numbered 1 through 6. he rolls the number cube twice. he rolls an odd number on the first roll. what is the probability that mario will roll an even number on the second roll?

By logic, we can say that the fact Mario scored an odd number on the first roll isn't going to affect the chance of getting an odd or even on the second roll, i.e. the events are independent;
Therefore, the chance of getting an even on the second roll is simply just the chance of getting an even on any roll;
We know a cube has six sides and assuming it is a fair cube, this means the chance of any given side facing upwards is 1/6;
There are 3 numbers which are even between 1 and 6 and 3 that are odd;
So, the chance of an even number facing upwards is:
3 * 1/6 = 3/6 = 1/2
In this case, this would also be the probability that the dice would give an odd number.