Commuting fraction of direct product is product of commuting fractions

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 $$p_1p_2$$.

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 $$p_1p_2\dots p_n$$.