Both events happen with probability 1/2: there are 3 even numbers and 3 odd numbers in a die.
Since the two events are also independent (the outcome of the first die doesn't affect the outcome of the second), we have to multiply those probability.
So, you roll an odd number on the first die and an even number on the second die with probability
[tex]\dfrac{1}{2}\cdot\dfrac{1}{2}=\dfrac{1}{4}[/tex]
