Each individual in a population of size $n$ is assigned a positive number as its weight. $k$ of the $n$ are sampled without replacement, with the individuals remaining at the time of each selection chosen with probabilities proportional to their weights. It is shown that for two fixed individuals, the events that each is in the sample can be positively correlated.
"A Counterexample to a Correlation Inequality in Finite Sampling." Ann. Statist. 17 (1) 436 - 439, March, 1989. https://doi.org/10.1214/aos/1176347027