  Let $p$ be a prime and $b(x)$ be an irreducible polynomial of degree $k$ over
$\mathbb{F}_p$. Let $d\geq 1$ be an integer. Consider the following question:
Is $b(x^d)$ irreducible? We derive necessary conditions for $b(x^d)$ to be
irreducible. Further, when the necessary conditions are satisfied, we obtain
the probability for $b(x^d)$ to be irreducible.
