Random Sampling in Milk Bottle Production

In the context of milk bottle production, the Department of Public Health requires a random sample of $k$ bottles from your factory. A probability-setting device, adjustable from 0 to 1, is at your disposal, determining the likelihood of selecting a given bottle. Your objective is to employ this device to obtain $k$ milk bottles from the production line, ensuring that each bottle is chosen with the same probability. Moreover, you have the flexibility to adjust the probability for each individual bottle as necessary. How can you effectively use the probability-setting device to meet these requirements and achieve a representative sample for regulatory compliance? It is noteworthy that the total number of milk bottles in the product line is unknown.