If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is -

The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other.
Let the event of getting either both even or both odd
Then
$$\eqalign{ & P\left( {\overline E } \right) = \frac{{18}}{{36}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2} \cr & P\left( E \right) = 1 - \frac{1}{2} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{2} \cr} $$