A counterexample is given to a proposition of Marshall and Olkin (1974, Ann. Statist.) describing a probability bound. A theorem which gives the conditions under which mixtures of associated random variables remain associated, is stated. This provides a method to obtain the required bound.
"On a Probability Bound of Marshall and Olkin." Ann. Statist. 6 (1) 232 - 234, January, 1978. https://doi.org/10.1214/aos/1176344082