  A subset $X$ of a groupoid is said to be deficient if $|X \cdot X|\leq |X|$.
It is well-known that the probability that a random groupoid has a deficient
$t$-element set with $t\geq 3$ is zero. However, as conjectured in [4], we show
that the probability is not zero in the case of sets of two elements and
calculate the exact value. We explore some generalisations on deficient sets
and their likelihoods.
