Commuting fraction of direct product is product of commuting fractions

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 $p_1p_2$.
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 $p_1p_2\dots p_n$.