Approximate bias of the estimated proportion in group testing

The maximum likelihood estimator for estimating proportions by group testing is biased. An expression for the approximate bias has been previously presented, which enables the creation of a less biased estimator by removing the term of (O(n^{-1})). However, in this previous work the term of (O(n^{-2})) was incorrectly derived. This note gives a correct derivation, and examines the relative contribution of the two terms.