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

Answer: Option B

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
$$\begin{array}{rl}& P\left(\overline{E}\right)=\frac{18}{36}\\ & =\frac{1}{2}\\ & P\left(E\right)=1-\frac{1}{2}\\ & =\frac{1}{2}\end{array}$$