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For 
$G$ a finite non-Abelian group we write 
$c(G)$ for the probability that two randomly chosen elements commute and 
$k(G)$ for the largest integer such that any 
$k(G)$-colouring of 
$G$ is guaranteed to contain a monochromatic quadruple 
$(x,y,xy,yx)$ with 
$xy\neq yx$. We show that 
$c(G)\rightarrow 0$ if and only if 
$k(G)\rightarrow \infty$.
