Commuting fraction of direct product is product of commuting fractions

Statement

For two groups

Suppose $G_{1}$ and $G_{2}$ are finite groups, the commuting fraction of $G_{1}$ is $p_{1}$ and the commuting fraction of $G_{2}$ is $p_{2}$. Then, the commuting fraction of the external direct product $G_{1}\times G_{2}$ is the product $p_{1}p_{2}$.

For multiple groups

The commuting fraction of an external direct product is the product of the commuting fractions of each of the direct factors.

In symbols, if $G_{1},G_{2},\dots ,G_{n}$ are finite groups and $p_{1},p_{2},\dots ,p_{n}$ are their commuting fractions, then the external direct product $G_{1}\times G_{2}\times \dots \times G_{n}$ has commuting fraction equal to the product $p_{1}p_{2}\dots p_{n}$.